2. Optimization Section 4.7

3. Optimization the process of finding an optimal value – either a maximum or a minimum under strict conditions

4. Problem Solving Strategies 1. Assign symbols to all given quantities and quantities to be determined - make sketch. 2. Write a primary equation for the quantity that is to be maximized or minimized. 3. Reduce the primary equation to one single independent variable. 4. Determine the domain 5. Use calculus to find the max or min 6. VERIFY!!!!!!

5. Example #1 A man wants to plant a rectangular garden along one side of his house, with a picket fence on the other three sides of the garden. Find the dimensions of the largest garden that can be enclosed using 40 feet of fencing.

6. Example #2 A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of the page are to be 1.5 inches, and the margins on the left and right are to be 1 inch. What should be the dimensions of the page so that the least amount of paper is used.

7. Example #3 Which points on the graph are closest to the point ?

8. Example #4 Four feet of wire is to be used to form a square and a circle. How much of the wire should be used for the circle to enclose the maximum total area?