Assignment 2

Assignment I (Due on Sept. 22 2015)

1. Consider the following LP problem.

MAX: 3x1+2x2

Subject to: 3x1+2x2≤300

6x1+3x2≤480

3x1+6x2≤480

x1,x2≥0

a. Sketch the feasible region for this model.

b. What is the optimal solution?

c. Identify any redundant constraints in this model.

2. Sanderson Manufacturing produces ornate, decorative wood frame doors and windows. Each item produced goes through three manufacturing processes: cutting, sanding, and finishing. Each door produced requires 1 hour 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 all doors produced can be sold for a profit of $500, and all windows can be sold for a profit of $400.

a. Formulate an LP model for this problem.

b. Sketch the feasible region.

c. What is the optimal solution?

3. The Quality Desk Company makes two types of computer desks from laminated particle board. The Presidential model requires 30 square feet of particle board, 1 keyboard sliding mechanism, 5 hours of labor to fabricate, and sells for $149. The Senator model requires 24 square feet of particle board, 1 keyboard sliding mechanism, 3 hours of labor to fabricate, and sells for $135. In the coming week, the company can buy up to 15,000 square feet of particle board at a price of $1.35 per square foot and up to 600 keyboard sliding mechanisms at a cost of $4.75 each. The company views manufacturing labor as a fixed cost and has 3,000 labor hours available in the coming week for the fabrication of these desks.

a. Formulate an LP model for this problem.

b. Sketch the feasible region for...