Learning Outcomes

1. Set up and solve optimization problems in several applied fields.

Textbook

• Chapter 4.7  Applied Optimization Problems

Textbook Assignment

• p. 451:    315, 316, 318-321 all, 335, 336

WeBWork Assignment

• Application-Optimization

Exit problems of the session

1. You have 800 ft of fencing to make a pen for hogs. If you have a river on one side of your property, what is thee dimension of the rectangular pen that maximizes the area?

2. A box with a square base and an open top must have a volume of 256 cubic inches. Find the dimensions of the box that will minimize the amount of material used (the surface area).

3. You are constructing a cardboard box with the dimensions  2m by 4m. You then cut equal-size squares from each corner so you may fold the edges. What are the dimensions of the box with the largest volume?

Key Concepts

• Steps of solving an optimization problem:
1.  Draw a picture and introduce variables.
2.  Find an equation relating the variables.
3.  Find a function of one variable to describe the quantity that is to be minimized or maximized.
4. Look for critical points to locate local extrema.

#### Videos and Practice Problems of Selected Topics

1. Minimizing sum of squares (7:34) What is the smallest possible sum of squares of two numbers, if their produce is ?
2. Box volume I (9:49) If you are making a box out of a flat piece of cardboard, how do you maximize the volume of that box?
3. Box volume II (8:59) Continuation of the previous problem.
4. Profit (11:26) Maximizing profits.
5. Cost of materials (12:39) Find the cost of the material for the cheapest rectangular storage container.