Study Guide: Math 160 - Chapter 5
- Write the requirements for a problem to be a standard maximization or standard minimization
- 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.
- Given a feasible region and a constant-profit (isoprofit) line, determine where the maximum
value occurs. Explain how you arrived at your answer.
- 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.
- 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.
- 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.
- 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.
- Form the dual problem (not system) from the minimization problem. Do NOT solve the
- Take a non-standard maximization or minimization problem and write the initial system from
it. Do NOT solve the system.
- 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.
- Problems 1 - 7 must be worked individually.
- The remainder of the test may be worked in groups of up to three 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
Take Home Portion (30 pts)
- Problem 5.4.28 (5 pts)
- Problem 5.4.44, part A (5 pts)
- Problem 5.5.24 (5 pts)
- Problem 5.5.46, part A (5 pts)
- Problem 5.6.42 - go ahead and solve (10 pts)
- The take home portion is due the day of the exam.