Study Guide: Math 160 - Chapter 5
- Write the requirements for a problem to be a standard maximization or standard
- 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.
- You are given a linear programming problem and asked to shade the feasible region. The
graph is drawn, you just need to shade the appropriate region. Then add slack variables
and/or subtract surplus variables to create a system that could be used in the geometric
approach (section 5.3) to create a table of decision, slack, and/or surplus variables and
determine if they're feasible or not.
- Given a table of intersection points, determine which points are feasible and which aren't.
Find the solution to the problem (maximum or minimum depending on the problem).
The solution includes the values of the variables and the objective function, not just the
point where it occurs.
- Given a feasible region and a constant-profit (isoprofit) line, determine where the
maximum value occurs. Explain how you arrived at your answer.
- You are 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.
- You are given the final tableau for a dual problem. Identify which variables are basic and
non-basic and give their values for both the dual (maximization) and original
- You are 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. Remember that the problem has the inequality constraints
in it; it does not contain slack, surplus, or artificial variables.
- You are given a tableau (not the initial). Identify which variables are basic and non-basic
and give their values. Identify which variable is basic in each row, indicate the pivot
column, find the appropriate ratios, indicate 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.
- Explain the pivot procedure. Know why the pivot column is chosen. Know why the
pivot row is chosen.
- Form the dual problem from the minimization problem. Do not solve the dual problem,
only set it up.
- You are given a geometric representation of a system. Identify which variables are basic
and non-basic for the indicated points. A tableau (not the initial) is given; identify which
point corresponds to the tableau, give the value of the objective function at that point, and
indicate where you would pivot to move to a specified point.
- The test is individual. There are no groups allowed.
- 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 only place you really need the calculator on the
test is to do division.
- There is a take home portion of the exam worth 30 points. It is due the day of the in-class
exam. The problems on the take home exam are listed below.
- To balance points properly, the total below is 100 points. That total will be multiplied by
0.70 and then the take-home point total added to that to get the final score.
Take Home Exam Problems
Work the following even problems from the textbook. You are free to use the simplex and pivot
programs once the tableaus are set up. You should write the initial and final tableaus, but you do
not need to write the intermediate tableaus unless you're using them to determine where to pivot
- 5.4.44 part a
- 5.5.46 part a
- 5.6.42, go ahead and solve. Hint: When properly setup, this problem can be turned into a
standard maximization problem and then the simplex program ran. That's why the "go
ahead and solve" instructions are there, the difficult part is setting it up properly.