## Study Guide: Math 160 - Chapter 5

1. Write the requirements for a problem to be a standard maximization or standard minimization problem.
2. Indicate how to convert a non-standard problem into the initial system. Know what to do with a <=, >=, and = constraints. Know how to handle a minimization problem.
3. Given a feasible region and a constant-profit (isoprofit) line, determine where the maximum value occurs. Explain how you arrived at your answer.
4. Given the final tableau for a dual problem, give the values of the decision and surplus variables for the primal problem.
5. Given a tableau (not the initial), indicate the values of all the variables (be careful), indicate which variables are basic, identify the pivot column, find the appropriate ratios, identify the pivot row, circle the pivot element, identify the entering variable, identify the exiting variable.
6. Form the dual problem from the minimization problem.
7. Given the initial tableau for a non-standard maximization problem, write the initial problem. This will require you to know all of the material in problem 2 and be able to reverse it to obtain the problem. The columns (variables) will not be named - you will need to be able to determine which are decision, slack, surplus, artificial, and objective based on the tableau.
8. Given a geometric representation of a system and a point on the graph, identify which variables are basic. Then identify which variable must enter and which variable must exit to move to another point on the graph. Move to another point and identify which variable is entering and which is exiting.
9. Explain the pivot procedure. Know why the pivot column is chosen. Know why the pivot row is chosen. Know how to find the change in the objective function.

### Notes:

• Problems 1 - 5 must be worked individually.
• The remainder of the test may be worked in groups of up to four people.
• The individual portion of the test must be returned to the instructor before forming groups.
• When you get into groups, it is often advantageous to split the workload, rather than all persons working together on a problem.
• Wherever possible, I have tried to compose the test so that the graphing calculator is useless and to test your actual understanding of the material, not your ability to run the simplex or pivot programs. In fact, the entire in-class portion of the test can be done without any calculator.
 # 1 2 3 4 5 6 7 8 9 Total Points 6 8 6 7 16 6 6 6 9 70

### Take Home Portion (30 pts)

1. Problem 5.4.28 (5 pts)
2. Problem 5.4.44, part A (5 pts)
3. Problem 5.5.24 (5 pts)
4. Problem 5.5.46, part A (5 pts)
5. Problem 5.6.42 - go ahead and solve (10 pts)
• The take home portion is due the day of the exam.