1. Announcement Test 2 is on this coming Tuesday (2/24) in IML computer lab – ARM 213/215 Students must schedule an exam time in WebCT It covers material through section 2.6 Electronic formula sheet will be available…see WebCT for preview Calculators up to TI-86 are welcome No books or notes Bring your student ID Test review is on Monday (2/23)

2. Section 2.5 – Optimization Problems

3. Suggestions for Solving an Optimization Problem (Page 179) 1.Draw a picture, if possible. 2.Decide what quantity Q is to be optimized. 3.Assign letters to the quantities that may vary. 4.Determine the “objective equation” that expresses Q as a function of the variables assigned in step 3.

4. 5.Find the constraint equation that relates the variables to each other and to any constraints that are given in the problem. 6.Use the constraint equation to simplify the objective equation in such a way that Q becomes a function of only one variable. Determine the domain of this function. 7.Sketch the graph of the function obtained in step 6 and use this graph to solve the optimization problem.

5. Problem 6, Page 180 Find two positive numbers x and y that maximize Q = x 2 y if x + y = 2

6. Problem 14, Page 180 Consider the problem of finding the dimensions of the rectangular garden of area 100 square meters for which the amount of fencing needed to surround the garden is as small as possible. a.Draw a picture of the rectangle and select appropriate letters for the dimensions b.Determine the objective and constraint equations. c.Find the optimal values for the dimensions.

7. Problem 17, Page 181 Find the dimensions of the closed rectangular box with square base and volume 8000 cubic centimeters that can be constructed with the least amount of material.