Chapter 6: Study Guide
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 =
- 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.
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