1. Directions Starting Mathematics for Business Decisions Part 2: Calculus and Optimization (i) Click on Slide Show in the top bar. (ii) Click on From Beginning in the next ribbon. (iii) When you are done reading each title page, move to the next page by clicking anywhere on the screen. (iv) When you reach the presentation’s Contents page, click on Easy Start, or on one of the icons to select a viewing option. 

2. Title page on the projects Business Decisions Computers Mathematical Models Teams Business Data The M athematical A ssociation of A merica Published and Distributed by With Interdisciplinary Multimedia Projects Part 2: Calculus and Optimization

3. Authors © 2009 by The Arizona Board of Regents for The University of Arizona. All rights reserved. Written By Dr. Richard B. Thompson Department of Mathematics University of Arizona Business Projects By Dr. Christopher G. Lamoureux Department of Finance University of Arizona Winner 2000 ICTCM Award for Excellence and Innovation Presented at the 2003 CNSF Exhibition, Washington, DC Mathematics for Business Decisions Part 2: Calculus & Optimization Mathematics for Business Decisions Part 2: Calculus & Optimization Mathematics for Business Decisions Part 2 Release 2, 2009

4. Contents Contents What would you like to see? Contents About Mathematics for Business Decisions Part 2: Calculus and Optimization Using The Electronic Text Course Activities Project 1. Marketing Computer Drives Project 2. Bidding On An Oil Lease What Mathematical & Computer Skills Will You Need? Solving Computer Problems Index        Acknowledgements and Credits Are you new to PowerPoint? Click on Easy Start.Easy Start  What is NEW inNEW Release 1.55? Check for Text Updates

5. Stop You did not make a selection from the list of topics on the preceding page. In order to study this material effectively you need to use hyperlinks, not simply move to the next page. Please click on Contents and then select the material that you wish to view. Contents

6. About Business Math CI  Mathematics About Mathematics for Business Decisions About Mathematics for Business Decisions Mathematics for Business Decisions is designed specifically for students majoring in business. It is the result of extensive collaboration between faculty members from the Eller College of Management and from the Department of Mathematics at the University of Arizona. (material continues) Business

7. About Business Math (material continues) Mathematics for Business Decisions is the foundation for your future career in business, showing you how to apply the language of mathematics to business problems, and how to use computers to help you do mathematics. The content, method of instruction, and computer software in this course are all carefully selected to prepare you for the job market and for future business courses. Top priority is given to the qualities that are desired by corporate recruiters. These include communication skills, creative problem solving skills, and the ability to work in teams. About Mathematics for Business Decisions: page 2 CI 

8. Part 2 of Mathematics for Business Decisions centers around two significant business problems and the tools, both mathematical and computer based, that are needed for their solutions. You will use the spreadsheet package Excel to assist you with the mathematics and with the presentation of your results. About Business Math (material continues) After the description of each project, teams of students make initial reports, indicating how they would attempt to solve the problem. These reports will be based upon common sense, intuition, and past business experience.  C About Mathematics for Business Decisions: page 3 I

9. About Business Math For several weeks after the initial reports, you will learn mathematical tools and computer skills that can be applied to the business case studies. While working on these, you will complete homework assignments. Using the new tools, each team will develop its final analyses of the projects and prepare both written and oral reports on their solutions. (material continues) Student presentations will be given in the current business style, using PowerPoint and Excel.  C About Mathematics for Business Decisions: page 4 I

10. About Business Math Class meetings will be used for presentation of the projects, discussion of the tools for their solutions, student activities, team reports, and instructor comments on the solutions. You will use this electronic text and its associated computer links to study the needed material. This can be done on any computer that is equipped with Windows XP or Vista, Office 2007, a CD drive, and an internet connection. Click on “Mathematics in Business Programs,” to access a report on the mathematics that is needed by business majors. This was prepared by a national panel of business college faculty members and administrators.Mathematics in Business Programs (material ends)  C About Mathematics for Business Decisions: page 5 I

11. Using The Electronic Text The PowerPoint, Excel, Word, and Media files for Part 2 of Mathematics for Business Decisions form a complete ELECTRONIC TEXT. This has many advantages over a traditional print and paper textbook.  Hyperlinks allow you to move easily between mathematical instruction, computer calculation, internet sites, and tutorial videos.  Computer animations clarify mathematical concepts.  Split screens allow you to view more than one page or application at the same time.  Electronic searching can locate any given word or phrase.  Use of the electronic text will prepare you for future electronic learning and will show you how to create your own business presentations.  Bytes on a CD weigh much less, take up less space, and cost less than a printed book! (material continues)  CI

12. Using The Electronic Text Using The Electronic Text: page 2 To realize the advantages of your electronic text, you must use it very differently than you would use a printed book. Here are some suggestions for the efficient use of your text, and some tips for getting the most benefit from the course files. Running The Text Files Moving Around In The Material Finding Specific Topics, Words, Or Pages Running Media Animations Viewing More Than One Page Or Application “Ask a Tutor” Videos List Of Course Files (material ends) What is the difference between an electronic text and a printed book?difference  C Click here. I

13. Electronic Text, Running Files Using The ElectronicText. Running The Files Using The Electronic Text. Running The Files RUNNING THE TEXT FILES  The text files run on PC’s with Microsoft Windows XP or Vista, and Office 2007.  PowerPoint, Excel, and Word files in the text contain boxes showing the text name, file release number, and date. Be sure that this information matches the assigned material in your course.  The PowerPoint file MBD Part 2.pptx, which you are now viewing, is the starting point for your course work. It contains project descriptions and a complete electronic index. Mathematical and computer instruction is given in the files MBD 2 Proj 1.pptx and MBD 2 Proj 2.pptx.  As soon as a presentation is opened, you can view the material and move around easily within the pages. However, animations and links to other pages, files, and applications will not operate until you start running the presentation. At times it is more efficient to leave a presentation in an open, but non-running, mode. In other cases you will want to run the presentation in order to take full advantage of its electronic features. Using The Electronic Text (material continues)  CI

14. Electronic Text, Running Files Using The ElectronicText. Running The Files: page 2 Using The Electronic Text. Running The Files: page 2  The easiest way to run a PowerPoint presentation is to click on the slide show icon in the toolbar at the bottom of the screen. Once the presentation is running, each click of the mouse button or press of the space bar will introduce a new feature or advance the presentation to the next page.  While a PowerPoint presentation is running, clicking the right mouse button will display a menu of options. Clicking on End Show will stop the presentation. You can also change to the non-running mode by pressing ESC. To end your viewing session, close all applications. Slide Show End Show (material ends)  Using The Electronic Text CI

15. Electronic Text, Moving Around (material continues) MOVING AROUND IN THE MATERIAL  Most pages contain some or all of the above buttons. Clicking on one of these while the presentation is running will move the presentation to the indicated location. Tools moves to a list of mathematical and computer tools for the current project. Contents moves to the table of contents. Index moves to an index for the entire course. The above buttons are inactive samples. Practice with the buttons at the bottom of the page.  With a presentation running, clicking on hot boxes or underlined hypertext will perform the indicated action. When you follow a link to another application, such as Excel, you may need to move around within that document in order to see the desired material. Previous page Tools Contents Index Next page CI  T C  Using The Electronic Text Using The ElectronicText. Moving Around Using The Electronic Text. Moving Around I

16.  On some computers, you may need to open applications, such as Excel, Word, or a browser, before following links to them.  To return to a PowerPoint presentation from another application, click on the colored border at the bottom of the screen, below the current application. In some versions of PowerPoint, you return by left clicking on the PowerPoint Slide button, located on the menu bar at the bottom of the screen. Try this by clicking on the Excel button, and then returning to this page.  If, for some reason, the Task Bar is not visible, pressing Ctrl- Esc will display both the Task Bar and the Start Menu. These can also be displayed by pressing one of the Windows keys that are located between the Ctrl and Alt keys at the bottom of your keyboard. Windows Electronic Text, Moving Around Using The Electronic Text (material continues)  Using The ElectronicText. Moving Around: page 2 Using The Electronic Text. Moving Around: page 2 C  I Excel

17. Electronic Text, Moving Around Using The Electronic Text (material ends)  When an exercise refers to a preceding exercise or example, the reference is usually a hot link that will take you directly to the previous material. You can click on the hypertext to get the information or see the methods that will be needed for the current exercise. The following plan provides a convenient way to return to the exercise on which you are currently working.  To return to a PowerPoint slide after following a link to another slide, right click anywhere in the screen to see a pull-down menu. Left click on Last Viewed. Using The ElectronicText. Moving Around: page 3 Using The Electronic Text. Moving Around: page 3  CI

18. Electronic Text, Finding (material continues)  Using The Electronic Text Using The ElectronicText. Finding Things Using The Electronic Text. Finding Things CI FINDING SPECIFIC TOPICS, WORDS, OR PAGES  While a presentation is running hyperlinks in the electronic index may be followed to locate specific topics in the PowerPoint text.  When a presentation is in the non-running mode, all occurrences of individual words or phrases can be located with PowerPoint’s built-in Find function. In Office 2007 select the Home tab and then click on Find. In earlier versions, click on Edit in the Main Menu, then on Find. Enter the words for which you want to search, then click on Find Next. It said, “Press any key.” Enter your word or topic.

19. Electronic Text, Finding (material continues) Using The Electronic Text  While a PowerPoint presentation is running, clicking the right mouse button will display a menu of options. To move to any given page, click on Go To Slide. This will display a list of slides that are close to your present location. To see other slides place the cursor over the carrot at the bottom of the list. The list will then scroll to the last slide in the presentation and display All Slides. Click on this to see a searchable list of all slides. Select the desired slide and click on Go To. Using The ElectronicText. Finding Things: page 2 Using The Electronic Text. Finding Things: page 2  CI

20. Slide Sorter View Electronic Text, Finding (material continues) Using The ElectronicText. Finding Things: page 3 Using The Electronic Text. Finding Things: page 3  When a presentation is in the non-running mode, pressing Page Up or Page Down on the keyboard moves the file to the preceding or following page, respectively. The Slide Sorter allows you to view thumbnail sketches of the pages and move to any selected page. Clicking on the Slide Sorter View icon at the lower left corner of the screen shows sketches. Double clicking on any page in the sorter selects that page for normal viewing. The presence of distinctive graphic images makes it easy to recognize a desired page.  Using The Electronic Text  CI

21.  The Slide tab in the Normal View allows you to view thumbnails of slides in a side panel. When a presentation is in the non-running mode, click on the Normal View icon at the lower left corner of the screen. Placing the cursor over a thumbnail will display its title. Clicking on any thumbnail will display the given slide in the main panel. The size of the side panel can be adjusted to display larger or smaller thumbnails. Normal View Electronic Text, Finding (material continues) Using The ElectronicText. Finding Things: page 4 Using The Electronic Text. Finding Things: page 4  Using The Electronic Text  CI

22. Outline  When a presentation is in Normal View in the non-running mode, clicking on the Outline tab will display a list of slide titles in the side panel. Clicking on any title selects that slide for normal viewing. Choosing a suitable working window allows you to use all of the features that are available in the non-running mode. Electronic Text, Finding Using The ElectronicText. Finding Things: page 5 Using The Electronic Text. Finding Things: page 5  Using The Electronic Text CI (material ends)

23. RUNNING MEDIA ANIMATIONS Set Windows Media Player as the default application to open *.avi files. When the player is opened, click on View and then select Skin Mode. To activate an animated media file (*.avi), while a PowerPoint presentation is running, click anywhere in the file picture area. This will launch Windows Medial Player and start the animation. To gain the most understanding from the mathematical animations, you will want to control the motion manually. To do this, click on the media player’s Pause button, and then use the slider to control the animation. To resume automatic motion, click on the Play button. Pause Button Play Button Slider Practice with the clock on the next page. Electronic Text, Animations (material continues)  Using The Electronic Text Using The ElectronicText. Animations Using The Electronic Text. Animations CI

24.  Run the animation automatically through its complete three hour cycle.  Pause the animation and use the slider to set the time for exactly 2:00 o’clock.  Restart automatic operation. Electronic Text, Animations (material ends)  Using The Electronic Text Using The ElectronicText. Animations: page 2 Using The Electronic Text. Animations: page 2 C Computer Problem? I

25. Click here to reduce size. Drag borders to adjust window size and shape. Electronic Text, Viewing  Using The ElectronicText. Viewing Using The Electronic Text. Viewing CI VIEWING MORE THAN ONE PAGE OR APPLICATION  By reducing the size of their windows, you can view the mathematics on a PowerPoint page and simultaneously perform Excel computations. To do this, the presentation must be open, but not running. (material continues) Using The Electronic Text

26.  You can open two different PowerPoint presentations, or two different slides in the same presentation. In Office 2007 click on View and then on Arrange All. In earlier versions, click on Window and then on Arrange All. Electronic Text, Viewing (material ends)  BONUS! The 20 point type used in this text allows small group viewing on monitors, large group viewing with projection, and easy reading on split screens and laptops. Using The Electronic Text Using The ElectronicText. Viewing: page 2 Using The Electronic Text. Viewing: page 2 CI

27. “ASK A TUTOR” VIDEOS Several pages in the course files contain “Ask a Tutor” boxes with a frequently asked question. Clicking anywhere in the upper box will open a short video that discusses the indicated material. The videos give informal answers that are similar to what you would get in a office visit with your instructor, or at a tutoring session. Avoid Computer Problems. Set Windows Media Player as the default application to open *.wmv files. When the player is opened, click on View and then select Skin Mode. To activate a video, while a PowerPoint presentation is running, click anywhere in the upper box of the picture. How do these videos work? Electronic Text, Ask a Tutor (material ends) Using The ElectronicText. ”Ask a Tutor” Using The Electronic Text. ”Ask a Tutor” Using The Electronic Text CI Try a sample video! Click anywhere in the upper box. To avoid a cluttered screen, minimize your browser once the video is playing.

28. Electronic Text, Course Files Using The Electronic Text Using The ElectronicText. Course Files Using The Electronic Text. Course Files C Excel Area Example.xlsx Auction Data.xlsx Auction Equilibrium.xlsm Auction Equilibrium.xlsm Auction Focus.xlsx Auctions.xlsx Binomial 2.xlsx Blank.xlsx Case Load.xlsx Comp Solution 2.xlsx Density 2.xlsx Differentiating.xlsm Dinners.xlsm Example 3.xlsx Exercise Data.xlsx Graph Examples.xlsx Excel (cont.) Graphing.xlsm Hospital.xlsx Integrating.xlsm Integration Example.xlsx Marketing Data.xlsx Marketing Focus.xlsm Midpoint Sums.xlsm Random.xlsx Salary.xlsx Sample Means.xlsx Samples.xlsx Shipping.xlsx Sizes.xlsx LIST OF COURSE FILES I (material continues) 

29. Electronic Text, Course Files (material ends) Excel (cont.) Skills 2.xlsx Slope.xlsx Variance.xlsx Media Dinners.avi Parabola.avi Practice 2.avi Sample Means.avi SD Prob.avi SD Sigmas.avi Sums.avi  List Of Course Files (cont.) Using The Computer TextPowerPoint MBD Part 2.pptx MBD 2 Proj 1.pptx MBD 2 Proj 2.pptx Word Preliminary 2.docx Rep Solution 2.docx Using The Computer Text. Course Files: page 2 CI

30. Course Activity Course Activities There are many different activities in Part 2 of Mathematics for Business Decisions. Select the topic that you wish to view. Teams And Projects Preliminary Report Studying The Tools Final Oral Report Avoiding Computer Problems Written Report Homework Study Plan Working With Your Team (material ends) CI

31. Course Activity, Teams & Projects TEAMS AND PROJECTS Each project will be introduced with a standard Class Project, which will be studied and solved as mathematical and computer tools are developed. During the first week of classes, small groups of students will be formed to work on Team Projects which are very similar to the Class Project. When a project is first introduced to the class, each team will be told how to obtain the details of its particular project. This information may be in the form of an Excel file, material to be downloaded from the internet, or data which is supplied by the instructor. Class Project Team Projects Teams Formed Preliminary Reports Solution Oral Reports Written Reports Tools and Homework Project Introduction Course Activities Course Activity. Teams & Projects C (material continues)  I

32. Immediately after projects are introduced, teams give preliminary oral reports. The class then develops and studies both mathematical and computer tools that will lead to sound business decisions, and will assist in project solutions. Focus on the Project sections follow work on most of the tools. These show how the given concepts apply to the Class Project. Homework problems ask each team to make the corresponding applications to its own Team Project. The Class Project is solved completely in the final Focus on the Project section. Student teams prepare both oral and written final reports. These emphasize the use of mathematics in their business decisions. Following the solution of each Class Project, we present an additional application of the project tools. This illustrates the use of the new concepts in a business setting that is completely different from that of the Class Project. Study of these “shadow projects” is optional. They may be used as reading assignments, or covered in the classroom while teams prepare their final repots on the Team Projects. Course Activity, Teams & Projects Course Activities (material ends) C Course Activity. Teams & Projects: page 2 I 

33. Course Activity, Preliminary Reports PRELIMINARY REPORT Shortly after a project is introduced each team will give a brief oral preliminary report on its project. After introducing its members to the class, a team will give a description of the team’s particular project, a discussion of the problem, and tentative decisions on the main project questions. The preliminary report should clearly indicate that your team has started to function as a problem solving group. It should also show that you have thought carefully about the project, and that you are beginning to develop some intuition about the business aspects of the situation. Do not worry if your team does not yet have an effective way to solve or even to attack the project. This ability will come as you study the computer and mathematical tools. In particular, you should NOT try to “read ahead” in a rushed attempt to study the tools. The preliminary report should be based upon study of the problem, your common sense, and business considerations. Since the report will be brief, your team must be well organized. Any use of PowerPoint or Excel should be kept at a very simple level. Course Activities (material ends) Course Activity. Preliminary Reports View a Video clip from a preliminary report in Part 2 of Mathematics for Business Decisions.Video CI

34. Course Activity, Tools STUDYING THE TOOLS To keep your team’s work on track, the final homework problem in most sections requires that you apply the given tool to your team project. Successful completion of these steps assures you that you are making satisfactory progress toward your report. Occasionally a team may head off in an inappropriate or completely wrong direction while working on its project. This can become a major problem if it is not discovered until the team is making its final report. For this reason it is usually wise for a team to discuss its conclusions with their instructor, prior to the report day. All mathematical and computer tools that will be needed for your project solution will be presented prior to the final section in each project. These concluding sections are substantial examples which use the earlier tools in much the same ways that you will use them in your project solutions. You should use the study time during the final example to complete work on your team’s project. Course Activities (material ends) Course Activity. Studying The Tools CI

35. Course Activity, Oral Report FINAL ORAL REPORT When all needed tools have been studied, each team will give a final report. This is to be a major presentation, given in the style that you will use in your future business career. Each team will prepare a written report and give an oral presentation, using a computer. The oral report should be built around a PowerPoint presentation, with links to Excel files, as needed for the project. All members of a team must actively participate in the report and every member must be able to explain any given mathematical or computer aspect of the report. Course Activities (material continues)  Click anywhere in the picture to view video clips from a final report from Part 2 of Mathematics for Business Decisions. Click on the pictures to view short excerpts from PowerPoint presentations. Course Activity. Oral Reports CI

36. Course Activity, Oral Report (material continues)  Oral reports will be evaluated on (i) the correctness and completeness of their contents; (ii) the ability of all team members to answer questions and explain what they have done; (iii) the extent to which they explore the Team Project beyond the basic level of the Class Project; and (iv) the organization, style, and business-like manner of the presentation. Oral presentations should introduce the team members and provide full information on the team’s project. All of the projects lead to one or more significant business decisions. Reports should clearly include the team’s final decisions, and should outline all of the major steps that were used in reaching those conclusions. Relevant mathematical formulas should be displayed and discussed. Any spreadsheets used in computations should be presented and explained.  Teamwork is critical. Plan ahead and hold group practice sessions before the time for class reports.  Be sure that every team member understands all of the business and mathematical ideas in your report.  Course Activities Course Activity. Oral Reports: page 2 CI

37. Course Activity, Oral Report (material ends)   Be professional, dressing and acting as you would in an important business meeting.  Speak directly to your audience. Do not simply read from notes or your PowerPoint file.  Avoid excessive use of sounds and animation in your report.  Do not attempt to show every step that you used in making your decision. Highlight the broad outline of your work.  Be prepared to explain any detail that might be needed to answer a question. Interpret all mathematical results in the business setting.  Assume that you are talking to a group of people who are familiar with the project tools, but not with your particular situation. Course Activities  If you use the course Excel files as models for your work, modify them so that they apply to your team’s project. Leaving in text boxes of general directions gives a very poor impression of your team’s effort. Course Activity. Oral Reports: page 3 CI

38. Course Activity, Computer Problems (material continues) AVOIDING COMPUTER PROBLEMS Preparing computer files which may have to be run on an unknown computer can be challenging. Here are some ideas that will help you avoid surprises when you give your reports.  When a computer encounters a type font which is not in its system, it substitutes one of its own fonts. This may or may not resemble the original font. To prevent odd looking presentations, use only standard type fonts which are supplied with Windows. The Times New Roman font is a very safe choice.  For good screen visibility use at least 20 point type fonts. This applies to equations as well as standard text.  File size can cause computer problems during your report. Huge files may not load quickly on a computer whose software differs from that which is on the machine that created the files. Limit the resolution of any graphics to at most 150 pixels per inch. The size of a PowerPoint file may increase each time that it is saved. Using Save As to save the file under a new name will correct this problem.  Course Activities Course Activity. Avoiding Computer Problems Course Activity. Avoiding Computer Problems CI

39. Course Activity, Computer Problems Course Activities (material ends)  Course Activity. Avoiding Computer Problems: page 2 CI If you want to copy sections of an Excel spreadsheet into your PowerPoint presentation, copy from Excel, then use Paste Special/Picture (Windows Metafile) to paste the object into PowerPoint. In particular, do not paste as a "Microsoft Excel Worksheet Object.” Incorrect use of copy/paste can create a simple PowerPoint presentation that contains over 26 MB. This may take as long as 35 minutes to open under some earlier versions of Office.  It is wise to avoid links to the internet in computer work for your reports. Such links are usually unnecessary, and only add to the risk of something going wrong.  Bring your report files to the classroom on a CD-R, a CD-RW, or a USB Drive. If you will need it, be sure to check that the presentation computer has a CD drive that reads CD-RW’s, or a USB port! Redundancy is essential. Have your presentation on at lease two different media.

40. Course Activity, Written Report Course Activities (material continues)  Course Activity. Written Report Course Activity. Written Report WRITTEN REPORT Each team will prepare a written report. This should be a self-contained document, describing the team’s particular project, presenting all calculations, indicating the key steps in its solution, and stating the team’s conclusions. It would also be appropriate to include any relevant details that were omitted from the oral report. Just as in a business report, the team’s written report should be word processed, and designed to make a lasting, positive impression on its readers. Personality and the ability to think on one’s feet are key points in an oral presentation. Completeness, correct writing, and attention to details are the hallmarks of an excellent written report. People may retain the written record of your work long after they have lost a clear recollection of your oral presentation. Successful teams often start by first preparing their written report. Once this is done, key points are extracted to form the basis for the computer files which will be used in the oral report. Team 1 PROJECT REPORT CI

41. Course Activity, Get Started Course Activities (material ends) Your work on a project starts with the team’s preliminary report. As each new tool is studied, apply it to your particular project and expand your report. If you wait until just before the final report to utilize the tools, your team will be badly rushed and there will be no time to correct any problems or misconceptions. Building the report as you progress through the material will take the pressure off of reporting. Use the assigned homework to help you prepare your reports. Using the tools with your project data is also one of the best ways to prepare for examinations over those tools. Click on the pictures to view short excerpts from Mathematics for Business Decisions written reports. Course Activity. Written Report: page 2 C  PDF copy: requires Adobe Acrobat Reader.  I

42. HOMEWORK Homework problems are spread throughout the PowerPoint files. Working all of these problems provides one of the best ways to master the mathematical and computer topics. Some of the problems ask you to explore or modify existing Excel files. Other questions ask you to create your own new spreadsheets. Many problems are to be solved with pencil and paper mathematics. Homework problems which are handed in for grading should be submitted as Word or Excel files, or as printout from such files. All work, including equations, must be computer generated or word processed. Complete sentences describing your solution must accompany the mathematical and computer work. Course Activity, Homework (material ends) Course Activities Course Activity. Homework CI

43. Course Activity, Study Plan STUDY PLAN  Read the project description and use Excel to look up the data. Take time to become familiar with the situation, to understand the data, and to find out exactly what you are asked to do with the project.  You will need both mathematical and computer tools in order to make effective decisions. Such topics are presented, following each project. Study all of the tools thoroughly, watching for ways to apply them to the project.  Both the mathematical and computer tools should be studied in the order in which they are presented in the PowerPoint file. (material continues)  Course Activities Course Activity. Study Plan CI

44. Course Activity, Study Plan  Each section contains examples. Read these carefully and be sure that you understand each one before continuing to work on the following material.  Some of the examples have buttons that you can use to view Excel worksheets or other ancillary material. Take advantage of this help by using all of the extra aids.  All sections contain several exercises. Stop and work each one of these (whether or not it is to be handed in) before continuing your study.  Some of the homework exercises provide the steps needed for your team’s preparation of its project reports. These are particularly important problems. (material continues)  Course Activities Course Activity. Study Plan: page 2 CI

45. Course Activity, Study Plan  Pay particular attention to the pages labeled “FOCUS on the project.” These show how each tool allows you to gain further insight into the problem that you are studying. on the project Calculus, Mathematics, Tests, Homework, Computers Business Decisions  (material ends) Course Activities Course Activity. Study Plan: page 3 CI

46. Course Activity, Teams WORKING WITH YOUR TEAM The ability to work effectively within a group of people is a major asset in the business world. It is also an important part of Mathematics for Business Decisions. You may encounter team members with any of the following traits.  The martyr: Willing to do all of the team work, with or without public complaint.  The slacker: Tries to get away without doing any of the work, but is willing to share in the credit.  The boss: Everything must be done in exactly his or her way.  The busy person: Cannot possibly fit team meetings into his or her full schedule.  The never follow through person: Promises to help, but never gets the job done. Course Activities (material continues)  Course Activity. Working With Your Team CI

47. Course Activity, Teams  The bright person: Seems to understand everything and be able to do any part of a project.  The slow person: Never seems to catch on to what is happening in class or with the project. You will find exactly the same mix of people in the rest of your business career. Learning to create an effective team out of diverse individuals may be a real challenge. Here are a few suggestions. Do not let one member dominate the team. Assert your right to influence group decisions and to participate fully in team activities. Do not accept the willingness of a few members to do most of the team work. If team homework is accepted, one person may be willing to do the problems. In this case, other team members will be unprepared for tests. Look for strengths in each team member and actively encourage everybody to participate. During project reports, the instructor is most likely to ask questions of any member who does not seem to be actively involved. Poor answers from one person reflect badly on the entire team.  Course Activities (material continues)  Course Activity. Working With Your Team: page 2 CI

48. Course Activity, Teams (material ends) Schedule team meetings at times and places which are convenient for every team member. If a member has a problem getting to meetings, ask him or her to pick a time for the next meeting. If problems develop within your team, attempt to work things out as a group. In the event that this does not seem to be working, keep your instructor informed of what is happening. If, despite being given ample opportunity and encouragement, a member has not participated in the preparation of a team report, other members have the right to omit his or her name from a written report or to exclude him or her from an oral presentation. Such action must only be taken as a last resort. However, you should not be intimidated into giving credit to someone who did not contribute to the team effort. The good news is that most teams learn to work together effectively. Different people bring diverse skills to the projects, creating a team that is stronger than its individual members. Students often report that teamwork provided support for their work in Mathematics for Business Decisions.  Course Activities Course Activity. Working With Your Team: page 3 CI

49. 1. Project Description Business Background Class Project 2. Mathematical Tools Demand, Revenue, Cost, and Profit Differentiation Integration Marketing Example 3. Computer Tools Graphing Functions Trend Lines Using Solver Project 1. Marketing Computer Drives A. B. C. A. B. C D. C. VideoVideo introduction by Prof. Christopher Lamoureux Department of Finance University of Arizona. Project 1. Marketing Computer Drives T I

50. Project 1. Background (material continues) Marketing Computer Drives. Business Background A company makes a positive profit when revenues from selling a product exceed the costs of its production. If a company is a monopoly, then the amount of its product that the company attempts to sell will affect the price that it can charge for the product. This contrasts with a perfect competitor, who cannot affect its good’s price by changing the amount that it attempts to sell. As an example of a perfect competitor, imagine the operator of a small farm. If she were to plant wheat instead of soybeans, there would be no effect on the price of either commodity. Pure monopolies are rare. The simplest examples are natural monopolies, such as public utilities, which are usually regulated by governmental agencies. Sometimes a new technology can give partial monopoly power to a company. Advertising also plays a role in enhancing a company’s monopolistic power by differentiating the company’s product from similar offerings of its competitors.  CI T

51. Project 1. Background (material continues) Marketing Computer Drives. Business Background: page 2 A monopolist generally has a down- ward sloping demand curve. This is the graph of the demand function, that relates the price which a company can charge for each unit of its product to the quantity of the product that it sells. No company can know its demand function exactly, but it can estimate the general properties of the function. The overall slope of a demand curve has business implications. For example, a medicinal drug might have a steeply dropping demand curve, whereas a new computer accessory seller might have a slowly dropping demand curve.  CI T

52. Project 1. Background (material continues) Marketing Computer Drives. Business Background: page 3 Let q be the number of units of a good that are sold, and let p be the price per unit at which that good is sold. The demand function relates these variables. A company’s revenue function is given by q  p. If a company sells a small amount of its good (small q), it can sell each unit for a high price (large p), but the total revenue may be small. If the company sells a very large quantity of its good (large q), then the unit price will be very low (small p). This may also result in low total revenue. In a monopolistic situation, the company wants to use its demand function to determine values for q and p that will produce the largest possible total revenue q  p.  CI T

53. Project 1. Background (material continues) Marketing Computer Drives. Business Background: page 4 When making goods, companies incur costs. The total cost function of production arises from the production process, and can be estimated by engineers and managers. There are fixed costs of production, which are incurred even if the company produces no units of its good. Variable costs are incurred on a unit-produced basis. The profit that a company makes is given by its revenue minus its costs. All companies confront the basic problem of determining the quantity of goods which should be produced and sold in order to maximize profit.  CI T

54. Project 1. Description, Class (material continues) Marketing Computer Drives. Class Project Card Tech, Inc. has just developed and patented a new type of external computer drive, the 12-GB. The new device has the ability to store 12 gigabytes of information on a rewriteable credit card sized wafer. Under the conditions of its patent, Card Tech has the exclusive right to produce and market the new technology during the coming three years. This gives the company temporary monopolistic power. The management at Card Tech wants to know how to price the 12- GB in such a way that it will produce the maximum profit during the coming year. They also need to know how many of the drives that they can expect to sell, and how much profit they might hope to realize from the sales. The Marketing Department at Card Tech estimates that there are 350 million potential customers in the national market for the coming year. They studied six test markets to determine the fraction of the potential buyers who would actually purchase the 12-GB, at various price levels. The results of these test markets are shown in the following table and in the Excel file Marketing Data.xlsx. Marketing Data.xlsx  CI T

55. Project 1. Description, Class Marketing Computer Drives. Class Project: page 2 (material continues) Obviously, the costs involved in manufacturing the 12-GB drives will play a major role in determining the appropriate price for the new product. The Production Department at Card Tech estimates that there will be fixed overhead costs of $135,000,000 during the coming year. The engineers at Card Tech made the following estimates for the production costs of several different quantities of drives. Past experience leads the Marketing Department to assume that the 12-GB drives will have a quadratic demand function.  CI T Marketing Data.xlsx

56. Project 1. Description, Class Marketing Computer Drives. Class Project: page 3 The first 800,000 drives will have production costs of $160 per drive. The next 400,000 drives will cost $128 per drive to produce. All drives after the first 1,200,000 can be produced for $72 per drive. We are to use the available information to analyze the pricing and production of 12-GB drives. 1. What price should Card Tech put on the drives, in order to achieve the maximum profit? 2. How many drives might they expect to sell at the optimal price? 3. What maximum profit can be expected from sales of the 12- GB ? 4. How sensitive is profit to changes from the optimal quantity of drives, as found in Question 2? 5. What is the consumer surplus if profit is maximized? (material continues)  CI T Marketing Data.xlsx

57. Project 1. Description, Class Marketing Computer Drives. Class Project: page 4 6. What profit could Card Tech expect, if they price the drives at $299.99? 7. How much should Card Tech pay for an advertising campaign that would increase demand for the 12-GB drives by 10% at all price levels? 8. How would the 10% increase in demand effect the optimal price of the drives? 9. Would it be wise for Card Tech to put $15,000,000 into training and streamlining which would reduce the variable production costs by 7% for the coming year? Card Tech is considering its options in terms of advertising and of putting more capital into its business. We are to analyze the following questions. (material continues)  CI T Marketing Data.xlsx

58. Project 1. Description, Team Marketing Computer Drives. Team Projects (material ends) Each team will receive an Excel file containing test market data, trend line directions, and production cost estimates for a new product. This data applies to the coming sales year for the product. Assuming that you have a temporary monopoly for the sale of all similar items, your team is to answer the following questions. 1. What price should be put on the new good, in order to achieve the maximum profit? 2. How many items might you expect to sell during the coming year at the optimal price? 3. What yearly maximum profit can be expected from sales of the new product? 4. How sensitive is profit to changes away from the optimal quantity of items, as found in Question 2? 5. What is the consumer surplus if profit is maximized? Your Excel file will also contain computational directions and additional questions on changes in demand and capital investments which should be answered in your team report.  CI T

59. Project 2. Bidding on an Oil Lease 1. Project Description Business Background Class Project 2. Mathematical Tools Distributions Variance The Sample Mean Normal Distributions Hospital Administration Example 3. Computer Tools Simulating Normal Random Variables A. B. C. D. E. A. B. A. C VideoVideo introduction by Prof. Christopher Lamoureux Department of Finance University of Arizona. Project 2. Bidding on an Oil Lease T I

60. Auctions are a common way to sell things. For example, the United States Treasury auctions Treasury Bills every week, and communication frequency bands are sold at auction. The auction mechanism is sensible when there is a variety of possible buyers who might each have different information about the item being sold, or when the item has an unknown value. The seller's objective in an auction is to get the highest possible price for the item being auctioned. The buyer hopes for the lowest price. There are several forms of auctions. In a first-price sealed-bid auction each bidder submits a sealed bid. The highest bidder gets the item and pays what she or he bid. In a second-price sealed-bid auction each bidder submits a sealed bid and the item goes to the bidder who submitted the highest bid. In this form of auction the winner pays the value of the second highest bid for the item. Project 2. Background Bidding on an Oil Lease. Business Background (material continues)  CI T

61. While working on this project you will develop a stable bidding strategy in a first-price sealed-bid auction. Such strategies were discovered in our setting in 2001, using the idea of a Nash Equilibrium. This concept was included in the work of John C. Harsanyi, John F Nash and Reinhard Selten for which they were awarded the 1994 Nobel Prize in Economics. An English (open outcry) auction is often used for art and livestock. In this case, an auctioneer asks for a starting bid and encourages the bidders to raise their bids. The item goes to the bidder who made the last bid, and is sold at that bid price. In a Dutch auction a clock starts at a high price and ticks down. When a bidder stops the clock, he or she gets the item at that price. Project 2. Background (material continues)  C Bidding on an Oil Lease. Business Background: page 2 Bidding on an Oil Lease. Business Background: page 2 I T

62. Project 2. Description, Class (material continues) 1. OIL AND GAS LEASES The rights to extract oil and natural gas from tracts of land or sea bottom are commonly sold in first-price sealed-bid auctions. In the United States, these leases are sold by the Mineral Management Service in the Department of the Interior. The Service’s Gulf of Mexico (GOM) Region handles lease auctions on the continental shelf in the Gulf. This area is further subdivided into western (WGOM), central (CGOM), and eastern (EGOM) sectors. The Mineral Management Service offers numbered sales in the CGOM area, with each sale consisting of several tracts. The sizes of the tracts vary, but they are generally close to 5,400 acres, or roughly 8-1/2 square miles each. The average number of tracts offered is around 3,900 (21,000,000 acres), with considerable variation. A company can bid on one or more of the tracts offered in a given sale. Typical bids cover 10% of the tracts that are offered. Bidding on an Oil Lease. Class Project  CI T

63. Project 2. Description, Class (material continues) Auctions in the CGOM region attract relatively large numbers of bidders, with an average of around 600 bids per numbered sale. Since companies bid on different selections of tracts, the number of bids on any given tract is much smaller. In most sales, bidding companies must post a security bond with their bid. The amount of the bond depends on the size of the bid, with some bonds as high as $3,000,000. For more information, including current sales, follow the link at the bottom of this page and visit the Mineral Management Service’s home page for Gulf of Mexico leases. The data in our Class Project is based upon information about leases in the CGOM sector that have been sold during the past ten years. Bidding on an Oil Lease. Class Project: page 2  C http://www.gomr.mms.gov I T

64. Project 2. Description, Class (material continues) 2. THE CLASS AUCTION We will consider 19 major oil exploration companies that are planning to bid on a set of 275 tracts in the central Gulf of Mexico sector. Each company employs geologists who will conduct tests and assays to estimate the amount of oil in, and the difficulty of extracting that oil from, the tracts. The lease will be sold in a first-price sealed-bid auction run by the Mineral Management Service. Bidding companies might be tempted to form bidding rings and share information about their proposed bids. To discourage such collusion among the bidders, the government sets a reserve price. If the highest bid is less than that price, the auction is closed and a lease for those tracts is not sold. Historical data is available on 20 prior leases for sets of tracts that are very similar to those which are to be auctioned. These sites have been developed and their proven values are now known.  C Bidding on an Oil Lease. Class Project: page 3 I T

65. Project 2. Description, Class (material continues) The proven values are given in the Excel file Auction Data.xlsx. The listed values represent the amount that a bidding company would have been willing to pay for the tract in order to make a fair and reasonable profit on the oil which was extracted. While the exchange of information between bidders, prior to an auction is discouraged, companies are free to compare data about tracts that have already been sold. To help in their future decision the 19 companies have decided to share their geologists’ prior estimates for the fair values of each of the 20 developed sale areas. These estimates, called signals, are also shown in the file Auction Data.xlsx. We will make several assumptions about the companies and their geologists. Assumption 1. The 19 companies will all bid in the auction, and they will be the only bidders for the tracts. Assumption 2. The geologists employed by each of the bidding companies are all equally expert and, on average, they can estimate the correct values of leases. Bidding on an Oil Lease. Class Project: page 4 Auction Data.xlsx  CI T

66. Project 2. Description, Class Specifically, each signal for the value of an undeveloped lease is an observation of a continuous random variable, S v, whose mean is the actual value, v, of the lease. Assumption 3. Except for their means, the distributions of the S v ’s are all identical. Assumption 4. All of the companies act in their own best interests, have the same profit margins, and have the same needs for business. Thus, the fair value of a lease is the same for all 19 companies. We are one of the 19 bidding companies, say Company 1. We must decide how much we should bid for drilling rights on the 275 tracts in the upcoming auction. Our company geologist estimates that the tracts will have a final proven value of s 1 = $264,900,000. s 1 estimates the amount that the company would be willing to pay for the lease in order to make a fair and reasonable profit on the oil which is extracted. This would sustain the company, neither weakening nor strengthening its circumstances. Bidding on an Oil Lease. Class Project: page 5 (material continues)  CI T Auction Data.xlsx

67. We will use the historical data to develop an understanding of the auction process that allows us to see what could be expected to happen if all 19 companies bid the same amounts as their signals. Next, we will explore several possible uniform bidding strategies that could be followed by all of the companies. These lead to the question of what our company should do, assuming that all of the other 18 companies follow a given bidding plan. We will answer this for several possible plans. Naturally, our rival companies are doing the same calculations. Our final goal is to determine a stable bidding strategy, with the following property. If all 19 companies follow this plan, no company could expect to improve its situation by deviating from the given strategy. To help develop insight into the auction process, classroom auctions may be held, with each student representing one of the bidding companies. Each of the other 18 companies has received an estimate of the lease’s value from their geologist. The amounts of these other signals are, of course, unknown to us. Project 2. Description, Class Bidding on an Oil Lease. Class Project: page 6 (material continues)  CI T Auction Data.xlsx

68. Project 2. Description, Team Bidding on an Oil Lease. Team Projects Each team of students will receive an Excel file giving a list of companies that will be bidding on a new lease that is similar to those in the historical data. The companies’ geologists’ prior signals for the 20 proven leases will be listed. In the team projects, these signals will completely replace the signals that are used in the Class Project. However, the same values for the 20 historical leases that are used in the Class Project, will also be used in the team projects. The file for each team will list its own Company 1 signal, s 1, for the next auction. Teams have three assignments.  Determine what would be expected to happen if each company bid the same amount as its signal.  Determine the Company 1 bid under several uniform bidding strategies, and explore the expected values of these plans.  Find a stable uniform bidding strategy that could be followed by all companies, without any chance for improvement. (material ends)  CI T Auction Data.xlsx

69. What Math & Computer Skills Will You Need? What Mathematical & Computer Skills Will You Need? What Mathematical & Computer Skills Will You Need? MATHEMATICAL BACKGROUND A good understanding of the mathematical concepts in Part 1 of Mathematics for Business Decisions is necessary for successful study of Part 2. Probability, which forms the backbone of Part 1, is the main prerequisite for Part 2 of Mathematics for Business Decisions. The key topics of random variables, probability mass functions, probability density functions, cumulative distribution functions, expected value, and random samples are reviewed briefly in Distributions, the first section of Project 1. This material is presented in a very compact form which is not intended to serve as an introduction to these topics. (material continues)  f X (x) = P(X = x) F X (x) = P(X  x) CI

70. Skills What Mathematical & Computer Skills Will You Need? page 2 (material continues)  COMPUTER SKILLS Part 2 of Mathematics for Business Decisions is not designed to serve as an introduction to computers. You will need considerable prior experience with Microsoft Windows and with the applications Excel and Word in the Microsoft Office Suite. Your Excel skills should include the entry of functions in cells and the plotting of data. You will need to create Word documents containing text, equations formed with an equation editor, and objects which are copied from Excel files. "Computer literacy" is a very elusive quantity. It is often difficult for a student to know if his or her background with computation is extensive or current enough to be adequate for Part 2 of Mathematics for Business Decisions. Anyone who is enrolled in the course, or who is thinking of enrolling in it, should use the following simple exercise to assess his or her computer skills and readiness for Part 2. You should allow an uninterrupted period of 40-50 minutes for the exercise. CI

71. Skills What Mathematical & Computer Skills Will You Need? page 3 (material continues)  1. Open Word and Excel, then create a new folder, named Practice, on the hard drive. 2. Open the course file Skills 2.xlsx and save that file in the folder Practice. Rename the file Computation.xlsx. Open the course file Preliminary 2.docx and save that file in the folder Practice. Rename the file Report.docx.Skills 2.xlsx Preliminary 2.docx 3. Open the Excel file Computation.xlsx, that you have saved, and follow the instructions that are given in the file. This will involve working in Computation.xlsx, copying material into the Word file Report.docx, and then adding text to that file. When you are done, save both of your files. CI

72. 4. If you have trouble with some part of the exercise use the application's electronic help to see if you can solve the problem. If you cannot figure out how to do a step, try to work around it and complete the exercise. 5. When you are done with your work and have saved your files, open the course files Comp Solution 2.xlsx and Rep Solution 2.docx, to view the solutions. These files contain comments and notes that will helpComp Solution 2.xlsxRep Solution 2.docx, you evaluate your computer readiness for Part 2 of Mathematics for Business Decisions. Study the solutions carefully, noting how each step was performed. Skills What Computer Skills Will You Need? page 4 (material continues)  CI

73. Skills (material ends)  What Computer Skills Will You Need? page 5 You can grade yourself! If your files are quite similar to the solutions, and if you completed the project in a reasonable amount of time, then you are probably in good shape to start the computer parts of Part 2 of Mathematics for Business Decisions. On the other hand, if the exercise took you more than an hour, or if you missed more than three of the ten main points, then it is very likely that you need more computer experience before you tackle the course. If you are unsure about how to evaluate the results of your exercise, or if you are not comfortable about your computer background, talk to your instructor. Attempting to learn the advanced computer skills that are taught in Part 2 of Mathematics for Business Decisions without a solid foundation in the basic aspects of Excel and Word would be very frustrating and time consuming. The most likely result of such an effort would be a low course grade, or outright failure. Do not miss out on the excitement of the business applications because you are having a continuing struggle with computers. CI

74. Solving Computer Problems (material continues)  “Have a computer problem?” “No, thanks, I just had one!!!” C Computer Problem? I The course files will run well on computers with most combinations of Microsoft Windows XP or Vista, and Microsoft Office Suite 2007. When a computer problem does occur, it is usually caused by an incomplete installation of software or some software component. If you experience a computer problem with the course files, you will probably find it discussed in the following list. Follow the instructions which are given for solving the problem. Blue boxes, such as, mark potential trouble spots in the text files. Click on a box to find a solution for the problem. Although the course files may run in several combinations of Windows and Office, they are Office 2007 files. Saving a course file as Office 2003 may cause it to run improperly in Office 2007.

75. Links to video clips do not work. Causes. You may not be connected to the Internet, your computer may not have a sound card, or you may not have set Windows Media Player as the default application to open *.wmv files. Solution. Connect to the Internet, install a sound card, or set Windows Medial Player as the default player. Hint: Minimize your browser once the video is playing. Course files do not open or do not run. Causes. You may be trying to run the material on a computer whose operating system is not Windows XP or Vista and Office 2007. The course files are not intended for use with Macintosh, Linux, or UNIX systems. Solution. Use a computer with the appropriate software. A utility that allows Office 2007 files to run in Office 2003 can be downloaded from Microsoft. This will enable most of the course files features. Click on the Downloads tab, and then download the Microsoft Office Compatibility Pack.downloaded Computer Problems (material continues) Solving Computer Problems: page 2  CI

76. An animation does not open or does not run properly when you click on it. Computer Problems Solving Computer Problems: page 3  CI (material continues) Cause. There is a problem with your computer’s default media player for *.avi files. The player may not work well in your system, or it may not be able to play this type of file. Solution. Select a Windows Medial Player as the default application to open *.avi files. In Computer or Windows Explorer right click on one of the *.avi course files. For example, use Practice 2.avi. Next, left click on Open With. This will display a pull down menu. Click on Choose Program and then select Windows Media Player. application. Check the Always use the selected program to open this kind of file box and then on OK. When you first open the player, click on View and then on Skin Mode.

77. You see odd symbols, such as , , or  ; where you would expect to see mathematical symbols; or you can not open the Symbol font. Computer Problems Solving Computer Problems: page 4 (material continues)  Causes. Various things, such as the installation of other software or hardware, can cause the failure of Microsoft Office applications to recognize the Windows font, Symbol. If this happens, applications commonly substitute the corresponding Wingdings characters for the mathematical characters in Symbol. For example, , , and  may appear as , , and .. Solution. If Symbol is available, this problem can be corrected by reinstalling Office. Insert the Office CD, run Setup, and select Reinstall. If Symbol is not available on your computer, you can download the font from the Mathematics for Business Decisions server. Click on fonts.exe, then on Save File. Save the self-extracting Zip file, fonts.exe, to a temporary location, put PowerPoint into the non-running mode, use the desktop or Windows Explorer to locate the file, and then double click on fonts.exe. Follow the directions to extract the files SYMBOL.TTF and MTEXTRA.TTF. Use Control Panel/Fonts/File/Install New Font to make the SYMBOL.TTF available.fonts.exe CI

78. Causes. Some installations of Microsoft Office Suite do not include Microsoft Equation 3.0. Your installation of Windows may not contain the TrueType font MT Extra. Solutions. Install the equation editor. For an initial installation of Office, run the Setup program on the Install CD and select a Custom installation. If you have a previous installation, choose the Install/Remove option. In either case, follow the directions to install the Equation Editor. Install the missing font. You can download the font from the Mathematics for Business Decisions server. Click on fonts.exe, then on Save File. Save the self-extracting Zip file, fonts.exe, to a temporary location, put PowerPoint into the non-running mode, use the desktop or Windows Explorer to locate the file, and then double click on fonts.exe. Follow the directions to extract the files SYMBOL.TTF and MTEXTRA.TTF. Use Control Panel/Fonts/File/Install New Font to make the MTEXTRA.TTF available.fonts.exe Microsoft Equation 3.0 does not appear on the Insert/Object pull down menu, or you see an error message and some large symbols are displayed incorrectly when you open the editor. Computer Problems Solving Computer Problems: page 5 (material continues)  CI

79. Computer Problems Solving Computer Problems: page 6 (material continues)  CI A label box is a solid black color. Problem 5 Cause. In some older versions of PowerPoint, repeated running of a presentation may cause a yellow label box to show a solid black fill. Solution. Select the box, then click on Format on the main PowerPoint ribbon. Click on Shape Fill, click on No Fill. This will remove the black fill and reveal the text. Finally, repeat the above steps, but select yellow fill. This will restore the original appearance of the box. If the box is grouped with other objects on a page, you must ungroup the items before you can correct the color problem. To ungroup objects, select the group or one of its components, click on the Format tab, then select Group. Click on Ungroup. Correct the color fill problem and then regroup the objects. Problem 6

80. You are unable to save your work on an Excel file because it is labeled as Read Only. Computer Problems Solving Computer Problems: page 7 (material continues) Causes. The file property has been set to Read Only. This may have happened when the file was copied from a read only CD Solution. In My Computer or in Windows Explorer right click on the name or icon for the problem file. Select Properties from the pull down menu, and then click on General. Remove the check from Read-only, and then click on OK. If you copied the course files from a CD, you can select all of the files and remove all of their read only properties at the same time. Remove the check.  CI

81. Computer Problems (material continues)  You do not find Data Analysis or the function RANDBETWEEN on the Excel menus, an Excel file behaves oddly, or Histogram returns an error message. C Solving Computer Problems: page 8 I Causes. These Excel features are not loaded or are not operative. In such cases, an Excel file which uses Random Number Generation or RANDBETWEEN cannot be computed. In some systems, files whose names contain blank spaces cause a problem. The Histogram function can only be used in the same worksheet that contains its input range. Solutions. Click on the Office Button, then on Excel Options/Add- Ins. Select Manage Excel Add-Ins, then Go. Check the Analysis Tool Pack and Analysis Tool Pack - VBA boxes and then click on OK. If Analysis Tool Pack and Analysis Tool Pack - VBA do not appear on the pull down menu, under Add-Ins, you do not have a full installation of Excel. Reinstall the application. Avoid error messages by using Histogram in the same worksheet as its input range, or rename the file with a single name.

82. You do not find the utility Solver on the Excel menus. Computer Problems Solving Computer Problems: page 9  Causes. This Excel features is not loaded or is not operative. Solution. Follow the Add-In directions that are given in Problem 8 to enable the Solver Add-In.Problem 8 While working in one of the Office applications, characters change after you type them. For example, i becomes I, f(x) becomes F(x), or 2nd becomes 2 nd. CI (material continues) Cause. The application is using its AutoComplete or AutoCorrect features. Solution. Click on the Office Button then on Excel Options. Select Proofing/AutoCoreect Options or Advanced. Disable any automatic changes which you do not want the application to make for you. 

83. An Excel macro button does not run its macro. Computer Problems Solving Computer Problems: page 10  (material continues) CI Cause. The Macro Security Level is set at high or medium. Solution. Change the Macro Security Level. If there is one, close the security message and close any open Excel or PowerPoint files. Click on the Office Button. Office Button Select Excel Options from the bottom of the dialog box.

84. Computer Problems Solving Computer Problems: page 11 (material continues)  CI Click on Trust Center in the sidebar, then on Trust Center Settings under the Microsoft Office Excel Trust Center heading. Finally, select Enable all macros. Trust Center Trust Center Settings

85. Computer Problems Solving Computer Problems: page 12  (material ends) CI If the Developer tab is displayed, the security level can also be set by clicking on that tab, then on Macro Security/Macro Settings. If you are concerned about security problems with macros, other than those in Mathematics for Business Decisions, you may wish to reset the security level when you are not running course files.

86. Index A-B Bicycle shorts example 2-1382-138 Binomial random variable 2-3,2-3 2-13, 2-712-132-71 Buffalo steak dinner example 1-35, 1-41, 1-64, 1-1201-351-411-641-120 1-139, 1-1731-1391-173 Bug in random number generator 2-1762-176 C Central limit theorem 2-1172-117 Confidence interval 2-1282-128 Consumer surplus 1-1381-138 Control buttons 1515 Cost function 1-411-41 marginal 1-64, 1-681-641-68 County administrator example 2-123, 2-171, 2-1792-1232-1712-179 Course files, needed 2828 running 1313 Cumulative distribution function 2-2,2-2 D Data Analysis, running 8181 Demand function 1-351-35 marginal 1-701-70 Derivative 1-80, 1-219, 1-2201-801-2191-220 properties 1-891-89 Difference quotient 1-681-68 Differentiation 1-80, 1-219,1-801-219 1-220 properties 1-891-89 C IndexIndex E-LE-L M-P Q-T U-ZM-PQ-TU-Z T2T2 T1T1

87. Index E Expected value, continuous random variable 2-38 finite random variable 2-122-12 Exponential random variable 2-27, 2-42, 2-772-272-422-77 F-G-H Files needed 2828 Final reports, Oral 3535 Written 4040 Focus pages, Demand, Revenue, Cost, and Profit 1-521-52 Differentiation 1-1061-106 Focus pages (continued), Distributions 2-582-58 Integration 1-1991-199 Normal Distributions 2-1592-159 Simulating Normal Random Variables 2-1842-184 Using Solver 1-1301-130 Variance 2-942-94 Fundamental Theorem of Calculus 1-194, 2-1561-1942-156 I-J-K Income stream 1-181, 1-1891-1811-189 Integral 1-1571-157 L Loading Data Analysis 8181  Index: page 2 A-DA-D M-P Q-T U-ZM-PQ-TU-Z C T2T2 T1T1

88. Index M Macros 8383 Marginal, cost 1-64, 1-681-641-68 demand 1-701-70 profit 1-701-70 revenue 1-701-70 Mean, continuous random variable 2-38 finite random variable 2-122-12 sample 2-462-46 Midpoint sums, defined 1-1491-149 animation 1-1521-152 N Normal random variable 2-107,2-107 2-119, 2-1432-1192-143 O Omphaloskepsis 1-2181-218 P Parameter 2-47, 2-812-472-81 Preliminary reports 3333 Present value of income stream 1-185 Probability density function, definition 2-162-16 Probability mass function, definition 2-22-2 (P continues)  Index: page 3  A-DA-D E-L Q-T U-ZE-LQ-TU-Z C T2T2 T1T1

89. Index P (continued) Profit function 1-441-44 marginal 1-701-70 Project 1, class project 5454 team projects 5858 Project 2, class project 6262 team projects 6868 Q Quotation 2-2272-227 R Random variable, binomial 2-3, 2-13, 2-712-32-132-71 exponential 2-27, 2-42, 2-772-272-422-77 Running animations 2323 Reports, final oral 3535 final written 4040 preliminary 3333 Revenue function 1-371-37 marginal 1-701-70 S-T Sample mean 2-462-46 Standard deviation, continuous 2-752-75 finite random variable 2-702-70 sample 2-862-86 sample mean 2-922-92 Standard normal random variable 2-107, 2-1192-1072-119 (S-T continues)  Index: page 4  A-DA-D E-L M-P U-ZE-LM-PU-Z C T2T2 T1T1

90. Index S-T (continued) Standardized random variable 2-82 Symbol font 7777 U Uniform random variable 2-272-27 V-W-X-Y-Z Variance, continuous random variable 2-75 finite random variable 2-692-69 sample 2-852-85 sample mean 2-922-92  Index: page 5 A-DA-D E-L M-P Q-TE-LM-PQ-T C T2T2 T1T1

91. I would like to express my appreciation to the follow- ing people who have been of great help with the writing, teaching, and publication of Mathematics for Business Decisions Part 1a and its companion e-texts Mathematics for Business Decisions Parts 1 and 2, and Calculus for Business Decisions. Robert Condon, former Computer System Manager for the Mathematics Department at the University of Arizona, provided excellent computer support during the early stages of the project. Edward Alexander, Donald Barkouskas, Tina Deemer, Gregory Hartman, Deborah Hughes Hallett, Robert Indik, Thomas Kennedy, Joceline Lega, William McCallum, Nicholas Rogers, Eugene Smith, and Douglas Ulmer, University of Arizona; John Hagood and Janet McShane, Northern Arizona University; Darci Kracht, Frank Smith, and George Tonge, Kent State University; Mufid Abudiab, George Tintera, and Natalya Warner, Texas A & M University at Corpus Christi; John Grima, Glendale Community College; Julie Tarr and Yvonne Brown, Pima Community College; and Lawrence Morales, Seattle Central Community College; have provided many helpful comments and suggestions on the material. Acknowledgements Acknowledgements & Credits (material continues)  CI

92. Marilou Mendel has served as course coordinator for the entire program at the University of Arizona during its later years. Her contributions have been of great value. Much of the success that the e-texts have enjoyed at the University of Arizona has been due to strong support from the Eller College of Management. Particular appreciation is owed to the Associate Dean for Undergraduate Programs, Pamela Perry. It has been a pleasure to work with The Mathematical Association of America. In particular, former Associate Executive Director, Donald J. Albers, has provided strong support and encouragement. Staff members Tonya Hahn, Kara Keller, Elaine Pedreira, Martha Pennigar, and Beverly Ruedi, have been very helpful. My wife, Shari Thompson, has contributed both great patience and much tangible assistance while this material was developed. Thank you, Richard B. Thompson Acknowledgements (material continues) Acknowledgements & Credits: page 2  CI Back to Contents

93. Acknowledgements Some of the photographic images in Mathematics for Business Decisions are taken from Hemera Photo-Objects Premium Image Collection, Version 1.0 by Hemera Technologies, Inc., P. O. Box 79093, Hull, Quebec, Canada J8Y6V2. Some of clip-art graphics in Mathematics for Business Decisions are taken from Arts & Letters by Computer Support Corporation, 15926 Midway Road, Dallas, Texas 75244. The authors express their appreciation to those students at the University of Arizona who have permitted the use of, and links to, their work in Mathematics for Business Decisions. Development and dissemination of this material has been partially supported by a grant from the National Science Foundation. Acknowledgements & Credits: page 3 (material ends)  CI

94. Easy Start Getting around in PowerPoint is as easy as 1 - 2 - 3 - 4! 1. To advance to the next page, or to introduce the next effect on a page: Place the cursor in any blank area of the screen and left click. 2. To move to the preceding page: Left click on. Try it now. Move to the next page and then return. 3. To move to another page in the presentation, to another PowerPoint presentation, or to an application (such as an Excel file): Left click on action boxes, such as, or on underlined text.underlined text 4. To return to PowerPoint from an application: Left Click on the strip of the PowerPoint screen that appears below the application screen. In some versions, you return by left clicking on the button Power- Point Slide, located on the menu bar at the bottom of the screen. Try it now. Go to Excel and then return.  Excel (material continues) If the cursor is hidden, wiggle the mouse, or right click and select Arrow under Pointer Options. Back to Contents 

95. Easy Start Back to Contents  Easy Start: page 2 Now that you have practiced the basic maneuvers, you are ready to learn the more sophisticated techniques which will help you study Part 2 of Mathematics for Business Decisions. To return to the regular course material, click on the red “Back to Contents box” at the bottom of this page. Once at the contents page, you might want to click on the hand next to About Mathematics for Business Decisions Part 2: Calculus and Optimization That section gives general information about the purpose and content of the course. After that, you should click on the hand next to Using The Electronic Text. That will display detailed instructions for using all of the course materials. Good luck with your work! (material ends)

96. Difference Weight: 4 pounds, 12 ounces Volume: 165 cubic inches Cost: $$$$$ You Can:  Riffle through the pages to find a topic.  Use the index and then turn pages to find a topic.  Flip back and forth between two pages.  Put it down and find a computer for computation. Weight: 2 ounces Volume: 3 cubic inches Cost: $$$$$ You Can:  View thumbnails andthumbnails click to see a page.  Click on a topic in the electronic index.electronic index  Split the screen to view twoSplit the screen pages at the same time.  Click on a link to compute incompute Excel. Using The Electronic Text What Is The Difference? What are the differences between a paper and print book and an electronic text? C (material ends) I

97. NEW IN RELEASE 2  All files are in the Office 2007 formats: *.pptx, *.xlsx, *.xlsm, or *.docx. Screen captures and Excel directions apply to Office 2007.  The data in Project 2, Bidding on an Oil Lease, is based upon actual auctions of oil and gas leases during the last 10 years by the Mineral Management Service in the Central Gulf of Mexico Sector.  All video clips are now in the *.wmv file format. These play conveniently in Windows Media Player and eliminate the need for RealPlayer.  New advanced level observations have been added to the Class Project for Marketing Computer Drives.  A link to Mathematics for Business Decisions’ web site has been added that allows access to any update files that may be available.  Any ambiguities or typographical errors that have been found in Release 1.55 have been removed. What Is New? Back to Contents (material ends) CI

98. CHECK FOR POSSIBLE UPDATES Future changes in linked web sites and modifications made in new versions of Office and Windows may require adjustments in the electronic text files of Mathematics for Business Decisions. If this occurs, new files will be posted on the Mathematics for Business Decisions web site. Click on the Download Free Updates box and then follow the link for your text release to see if there are any available updates and to download the most current files for your electronic text. Updates Update Text Files Back to Contents (material ends) C Download FREE Updates I

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