403L Final Exam Review Sheet
A frisbee manufacturing company makes three styles of frisbees: junior, regular and competition. The company produces frisbees by the case. Producing one case of junior models costs $300 and requires 5.5 hours of labor. Making one case of the regular model costs $350 and requires 7 hours of labor. The competition model costs $420 and requires 7.5 hours of labor per case. The company can spend $40,000 and has available 800 labor hours. The junior frisbees generate a profit of $325 per case, while the regular frisbees generate a profit of $345 per case and the competition frisbees generate a profit of $350 per case. How many of cases each type of frisbee should the company make in order to maximize its profits?
a) Set up the initial simplex tableau for the following linear programming problem.
Maximize:
Subject to:
.
b) Perform one iteration of the simplex method.
c) Are you now at the optimal solution?
Minimize:
Subject to:
, .
(a) On the graph below, shade the feasible region and label it with the letters ``FR''.
(b) Determine the coordinates of the corner points of the feasible region and find the optimal solution(s).
Maximize:
Subject to:
, .
(a) On the graph below, shade the feasible region and label it with the letters ``FR''.
(b) Let , and be slack variables for the first, second and third constraints listed above. The simplex tableau
corresponds to a basic feasible solution. Which one? (i.e. Determine values of all the variables.) What are the the basic and non-basic variables of this basic feasible solution? Circle the point on the graph which corresponds to this solution.
(c) Perform one iteration of the simplex method to arrive at a new basic feasible solution. What is the new basic feasible solution? Is this new solution optimal? Circle the point on the graph which corresponds to this solution.
How can you tell that your friend made a mistake somewhere?