Optimization Review- 3-D This template can be used as a starter file for presenting training materials in a group setting. Sections Right-click on a slide to add sections. Sections can help to organize your slides or facilitate collaboration between multiple authors. Notes Use the Notes section for delivery notes or to provide additional details for the audience. View these notes in Presentation View during your presentation. Keep in mind the font size (important for accessibility, visibility, videotaping, and online production) Coordinated colors Pay particular attention to the graphs, charts, and text boxes. Consider that attendees will print in black and white or grayscale. Run a test print to make sure your colors work when printed in pure black and white and grayscale. Graphics, tables, and graphs Keep it simple: If possible, use consistent, non-distracting styles and colors. Label all graphs and tables. Review- 3-D

If something is made as small as possible it is called minimized Definition If something is made as small as possible it is called minimized If something is made as large as possible It is called maximized

Steps 1. Identify quantity to be maximized or minimized 2. Draw and label the figure 3. Primary equation 4. Represent all quantities with one variable 5. Find the max or the min 6. Check to see if answer is reasonable. Check interval

1) Find the rectangle of perimeter 60 with the largest area.

2) Find the rectangle of largest area inscribed in the parabola

3) An open box is to be made from a 8” by 12” piece of cardboard by cutting squares out of the corners and folding up the sides. Find the dimensions of the box if the volume is to be maximized.

4. A can is to be made in the shape of a right circular cylinder 4. A can is to be made in the shape of a right circular cylinder. It the cylinder will hold 500 cm3 find the dimensions of the can that will minimize the surface area.

5) How close does the graph of come to the point (4, 2)?

6) A farmer has 500 meters of fencing and wants to fence off a rectangular field with a semi-circle at one end. What are the dimensions of the field that has the largest area?

Home Work Optimization worksheet and worksheet 3-D Use a section header for each of the topics, so there is a clear transition to the audience. Optimization worksheet and worksheet 3-D