This LP model was solved by computer:

The following information was obtained from the output. The ranges were also computed based on the output, and they are shown as well.

a. Which decision variables are basic (i.e., in solution)?

b. By how much would the profit per unit of product 1 have to increase for it to have a nonzero value (i.e., for it to become a basic variable)?

c. If the profit per unit of product 2 increased by $2 to $22, would the optimal production quantities of products 2 and 3 change? Would the optimal value of the objective function change?

d. If the available amount of labor decreased by 12 hours, would that cause a change in the optimal values of the decision variables or the optimal value of the objective function? Would anything change?

e. If the available amount of material increased by 10 pounds to 210 pounds, how would that affect the optimal value of the objective function?

f. If profit per unit on product 2 increased by $1 and profit per unit on product 3 decreased by $.50, would that fall within the range of multiple changes? Would the values of the decision variables change? What would be the revised value of the objective function?

Transcribed Image Text:

Maximize 15x + 20x + 14x3 Subject to: Labor Material Machine 5x + 6x + 4x3 10x + 8x2 + 5x3 4x1 + 2x + 5x3 X1, X2, X3 where < x = quantity of product 1 X= quantity of product 2 x3 = quantity of product 3 210 hours 200 pounds 170 minutes 0