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), 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.
  5. Given the final tableau for a dual problem, give the values of the decision and slack variables for the dual (maximization) and decision and surplus variables for the primal (minimization) problems. Identify the number of problem constraints and decision variables in the original problem. Select (multiple choice) an objective function that could go with this problem - hint, the objective function must check when the values of the variables are substituted back into it.
  6. 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.
  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, similar to what you would see from the calculator - you will need to be able to determine which are decision, slack, surplus, artificial, and objective based on the tableau.
  8. Form the dual problem (not system) from the minimization problem. Do NOT solve the problem.
  9. Take a non-standard maximization or minimization problem and write the initial system from it. Do NOT solve the system.
  10. Given a geometric representation of a system and a point on the graph, identify which variables are basic at that point. Identify which variable must exit and enter in order to move from one point on the graph to another point on the graph.

Notes:

# 1 2 3 4 5 6 7 8 9 10 Total
Points 6 8 4 15 8 6 6 5 5 7 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)