A company makes two types of motors: Model A and Model B. Both models require work on Wiring Machine and Drilling Machine. Every week, the factory has limited hours of use on Wiring Machine and Drilling Machine. The company wants to find the best possible combination in order to maximize its profit. After using Excel Solver to solve an LP model, we obtain the following two tables from the Sensitivity Report. Using only the information in this report, answer the following questions.

If you believe you don't have enough information to give an exact answer, you can say that.

Variable Cells

Final

Reduced

Objective

Allowable

Allowable

Cell

Name

Value

Cost

Coefficient

Increase

Decrease

$K$13

Quantity of Model A

0

-25

20

25

1E+30

$L$13

Quantity of Model B

60

0

30

1E+30

16.66667

Constraints

Final

Shadow

Constraint

Allowable

Allowable

Cell

Name

Value

Price

R.H. Side

Increase

Decrease

$L$21

Availability of Wiring

120

15

120

20

120

$L$22

Availability of Drilling

60

0

70

1E+30

10

a. (1) Calculate the range of optimality for each variable. (2) Explain the value of reduce cost for the quantity of Model A.

b. (1) Calculate the range of feasibility for each constraint. (2) Explain the value of shadow price for the availability of Wiring.

c. Due to the competition, the company has to reduce the price of one unit of Model B motor by $2. (1) How would this change affect the optimal solution? (2) What would be the optimal profit after the change? Show your work and/or support your answer with appropriate data.

d. Assume the change in Part c has never occurred. The company is able to lease an additional Wiring Machine at the cost of $6/hour. (1) What would be the optimal profit if the company leases the additional Wiring Machine for 10 hours every week? Can you also predict the optimal solution? (2) What will be the optimal solution and profit, if the company leases the additional Wiring Machine for 25 hours every week?