Learning Outcomes

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


  • 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. $\rhd$ Minimizing sum of squares (7:34) What is the smallest possible sum of squares of two numbers, if their produce is $-16$?
  2. $\rhd$ 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. $\rhd$ Box volume II (8:59) Continuation of the previous problem.
  4. $\rhd$ Profit (11:26) Maximizing profits.
  5. $\rhd$ Cost of materials (12:39) Find the cost of the material for the cheapest rectangular storage container.