Given this linear programming model, solve the model and then answer the questions that follow.

Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc.

Subject to:

Machine 5 x 1  + 4 x 2  + 3 x 3

≤

160 minutes Labor 4 x 1  + 10 x 2  + 4 x 3

≤

288 hours Materials 2 x 1  + 2 x 2  + 4 x 3 ≤ 200 pound s Product 2 x 2

≤

16 units x 1 , x 2 , x 3

≥

0

a. Are any constraints binding? If so, which one(s)?

b. If the profit on product 3 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain.

c. If the profit on product 1 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain.

d. If 10 hours less of labor time were available, what would the values of the decision variables be? The objective function? Explain.

e. If the manager decided that as many as 20 units of product 2 could be produced (instead of 16), how much additional profit would be generated?

f. If profit per unit on each product increased by $1, would the optimal values of the decision variables change? Explain. What would the optimal value of the objective function be? LO.1