1. A clothier makes coats and slacks. The two resources required are wool cloth and labor. The clothier has 150 square yards of wool and 200 hours of labor available. Each coat requires 3 square yards of wool and 10 hours of labor, whereas each pair of slacks requires 5 square yards of wool and 4 hours of labor. The profit for a coat is $50, and the profit for slacks is $40. The clothier wants to determine the number of coats and pairs of slacks to make so that profit will be maximized. Formulate a linear programming model for this problem. Define x₁ as the number of coats, x₂ as the number of pairs of slacks, and Z as the total profit. Which of the following model formulations is correct?

a. Maximize Z=50x₁+40x₂ subject to 3x1+5x2<=150 10x1+4x2<=200 x1, x2>=0

b. Maximize Z=50x₁+40x₂ subject to 3x1+5x2>=150 10x1+4x2>=200 x1, x2>=0

c. Minimize Z=50x₁+40x₂ subject to 3x1+5x2<=150 10x1+4x2<=200 x1, x2>=0

d. Minimize Z=50x₁+40x₂ subject to 3x1+5x2>=150 10x1+4x2>=200 x1, x2>=0

2. Plot lines for each constraint and then identify the feasible solution area. Which of the following points is NOT among the corner points of the feasible solution area?

a. (0, 30)

b. (20, 0)

c. (10.53, 23.68)

d. (50, 0)

3. The optimal solution to the model is:

a. (0, 30)

b. (10.53, 23.68)

c. (20, 0)

d. (50, 0)

4. the optimal objective function value (total profit) based on the optimal solution is:

a. 1200

b. 1000

c. 2500

d. 1473.68