Management Science LP Problem

Management Science

9. Solve the following LP problem graphically by enumerating the corner points.
MIN:          5X1 + 20X2
Subject to: X1 +   X2 ≥ 12
2X1 + 5X2 ≥ 40
X1 + X2 ≤ 15
X1, X2     ≥ 0

Management Science LP Problem

10. Consider the following LP problem.
MAX:              3X1 + 2X2
Subject to:     3X1 +   3X2 ≤ 300
6X1 + 3X2 ≤ 480
3X1 + 3X2   ≤ 480
X1, X2 ≥   0

12. Solve the following LP problem using level curves.
MAX:                 4X1 + 5X2
Subject to:            2X1 + 3X2 ≤ 120
4X1 +   3X2 ≤ 140
X1 +     X2    ≥ 80
X1, X2      ≥   0

Management Science LP Problem

16. Refer to the previous question. Suppose that Electrotech’s management decides that they need to make at least 20 generators and at least 20 alternators.
a. Reformulate your LP model to account for this change.
b. Sketch the feasible region for this problem.
c. Determine the optimal solution to this problem by enumerating the corner points.
d. Suppose that Electrotech can acquire additional wiring time at a very favorable cost. Should it do so? Why or why not?

Management Science LP Problem

21. Sanderson Manufacturing produces ornate, decorative wood frame doors and windows. Each item produced goes through 3 manufacturing processes: cutting, sanding, and finishing. Each door produced requires 1 hour in cutting, 30 minutes in sanding, and 30 minutes in finishing. Each window requires 30 minutes in cutting, 45 minutes in sanding, and 1 hour in finishing. In the coming week Sanderson has 40 hours of cutting capacity available, 40 hours of sanding capacity, and 60 hours of finishing capacity. Assume that all doors produced can be sold for a profit of $500 and all windows can be sold for a profit of $400.