McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Table of Contents Chapter 1 (Introduction) Special Products Break-Even Analysis (Section 1.2)1.2 – 1.6 Advertising Problem (UW Lecture)1.8 – 1.21 An illustration of the management science approach to a problem. At the University of Washington, this is the very first lecture in the core MBA class on management science. While it includes some advanced topics (Solver, nonlinear objectives, etc.) it can be taught entirely on the spreadsheet in a very intuitive way, and has proven to be a good introduction to the power of Solver. The next several lectures then would need to “back up” and cover more of the fundamentals of linear programming, modeling, the Solver, etc.

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Special Products Break-Even Analysis The Special Products Company produces expensive and unusual gifts. The latest new-product proposal is a limited edition grandfather clock. Data: –If they go ahead with this product, a fixed cost of $50,000 is incurred. –The variable cost is $400 per clock produced. –Each clock sold would generate $900 in revenue. –A sales forecast will be obtained. Question: Should they produce the clocks, and if so, how many?

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Expressing the Problem Mathematically Decision variable: –Q = Number of grandfather clocks to produce Costs: –Fixed Cost = $50,000 (if Q > 0) –Variable Cost = $400 Q –Total Cost = 0, if Q = 0 $50,000 + $400 Q, if Q > 0 Profit: –Profit = Total revenue – Total cost Profit = 0, if Q = 0 Profit = $900Q – ($50,000 + $400Q) = –$50,000 + $500Q, if Q > 0

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Special Products Co. Spreadsheet

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Analysis of the Problem

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Management Science Interactive Modules Sensitivity analysis can be performed using the Break-Even module in the Interactive Management Science Modules (available on your MS Courseware CD packaged with the text). –Here we see the impact of changing the fixed cost to $75,000.

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Special Products Co. Spreadsheet

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., An Advertising Problem Parker Mothers is a manufacturer of children’s toys and games. One of their hottest selling toys is an interactive electronic Harry Potter doll. Some data: –Unit Variable Cost:$48 –Unit Selling Price:$65 –Fixed Overhead:$42,000 Parker Mothers has analyzed past data for the Harry Potter doll (and other similar toys), and determined that sales are affected by a number of factors: –the season (e.g., more at Christmas, more when a new Harry Potter book or movie is released, etc.), –the size of the sales force devoted to the product, –the level of advertising. Question: What should the advertising budget for the Harry Potter doll be? (Proposal: $50,000)

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Predicting the Sales Level After performing a statistical regression analysis, they estimate that sales for the quarter will be approximately related to the season and advertising budget, as follows: Seasonality Factors: –Q1:1.2 (publication of new Harry Potter book) –Q2:0.7 –Q3:0.8 –Q4:1.3 (Christmas and expected release of new Harry Potter movie) Effect of Advertising:

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Spreadsheet for Quarter 1

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Trial Solutions

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., The Excel Solver

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., The Optimized Solution

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Four Quarters Spreadsheet

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Four Quarters Solver Optimized

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Residual Effect

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Residual Effect (Solver Optimized)

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Solver Options

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Residual Effect (Solver Re-Optimized)

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Residual Effect with Budget (Optimized)

McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., Adding a Constraint in Solver