- Set up and solve optimization problems in several applied fields.
- Chapter 4.7 Applied Optimization Problems
- p. 451: 315, 316, 318-321 all, 335, 336
Exit problems of the session
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?
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).
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?
- Steps of solving an optimization problem:
- Draw a picture and introduce variables.
- Find an equation relating the variables.
- Find a function of one variable to describe the quantity that is to be minimized or maximized.
- Look for critical points to locate local extrema.
Videos and Practice Problems of Selected Topics
- Minimizing sum of squares (7:34) What is the smallest possible sum of squares of two numbers, if their produce is ?
- 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?
- Box volume II (8:59) Continuation of the previous problem.
- Profit (11:26) Maximizing profits.
- Cost of materials (12:39) Find the cost of the material for the cheapest rectangular storage container.