You will need to know the following definitions for the test. Certain problems will ask for the initial problem, others for the initial system, and still others for the initial tableau. Be sure to give the right one.

**Problem**: Stated as a problem with inequalities. Minimize or Maximize an objective function
subject to constraints. This is not a matrix.

**System**: Stated as a problem with the inequalities converted to equalities. Minimize or Maximize
an objective function subject to constraints. This is not a matrix.

**Tableau**: This is the matrix form of the linear programming problem.

- Graph a system of linear inequalities. Label the feasible region. Identify the corner points with a capital letter and name the ordered pair. Describe the region as bounded or unbounded.
- Given the number of slack, surplus, and artificial variables, decide the number of >=, <=, and = to constraints.
- Tell what the requirements are for being a standard minimization or a standard maximization problem are in terms of the type of constraints, the right hand side, and the objective function.
- Tell how to handle each of the three types of constraints. That is, what do you add or subtract to the equation and the objective function in each case.
- Given an initial tableau, perform the first pivot. This tableau involves big-M and as such artificial variables. Write the initial problem from the tableau.
- Work a standard maximization problem.
- Given a linear programming problem: Decide if it is in standard form or not. Write the initial system. Write the initial tableau. On the initial tableau, indicate which variables are basic for each row, compute the proper ratios to the right, indicate the pivot row, pivot column, and pivot element, indicate the entering variable and the exiting variable. Give the final tableau and the values of the variables.
- Form the dual problem for a minimization problem.
- Give the answers to the maximization (dual) problem and minimization (primal) problem from the final tableau of a dual problem.
- Solve a non-standard linear programming problem.

This will be a group exam. The first page (problems 1 - 6) will be worked individually. The remainder of the exam (problems 7 - 10) may be worked in groups of up to three people. The first page must be completed and turned in before groups may begin, but there is no time requirement before getting into groups. That is, if your group can do the first page in five minutes, then you can spend fifty-five minutes on the remainder.

Last updated: Sunday, June 30, 1996 at 9:30 PM

Send comments to james@richland.edu.