## 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 a tableau (not the initial) for a standard maximization problem, identify the number of slack variables and decision variables. Label the columns of the tableau with the appropriate variable names, identify which variables are basic and non-basic, give the value of each of the variables, identify a function that could be the objective function (multiple choice), and state whether or not the optimal solution has been found.
5. Given the final tableau for a dual problem, give the values of the decision and surplus variables and the value of the objective function for the original minimization problem.
6. 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, identify how much the objective function will increase after the pivot.
7. Form the dual problem from the minimization problem. Do not solve the dual problem, only set it up.
8. 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.
9. 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.
10. Explain the pivot procedure. Know why the pivot column is chosen. Know why the pivot row is chosen.

### Notes:

• The entire test in-class portion of the test is individual.
• 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.
• There is a take home portion of the exam. It is due the day of the in-class exam.
•  # 1 2 3 4 5 6 7 8 9 10 Total Points 6 8 4 10 7 10 6 9 6 4 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)