Davison Electronics manufactures two models of LCD televisions, identified as model A and model B. Each model has its lowest possible production cost when produced on Davison's new production line. However, the new production line does not have the capacity to handle the total production of both models. As a result, at least some of the production must be routed to a higher-cost, old production line. The following table shows the minimum production requirements for next month, the production line capacities in units per month, and the production cost per unit for each production line:

Let
AN = Units of model A produced on the new production line
AO = Units of model A produced on the old production line
BN = Units of model B produced on the new production line
BO = Units of model B produced on the old production line
Davison's objective is to determine the minimum cost production plan. The computer solution is shown in Figure 3.21.
a. Formulate the linear programming model for this problem using the following four constraints:
Constraint 1: Minimum production for model A
Constraint 2: Minimum production for model B
Constraint 3: Capacity of the new production line
Constraint 4: Capacity of the old production line
b. Using computer solution in Figure 3.21, what is the optimal solution, and what is the total production cost associated with this solution?
c. Which constraints are binding? Explain.
d. The production manager noted that the only constraint with a positive dual value is the constraint on the capacity of the new production line. The manager's interpretation of the dual value was that a one-unit increase in the right-hand side of this constraint would actually increase the total production cost by $15 per unit. Do you agree with this interpretation? Would an increase in capacity for the new production line be desirable? Explain.
e. Would you recommend increasing the capacity of the old production line? Explain.
f. The production cost for model A on the old production line is $50 per unit. How much would this cost have to change to make it worthwhile to produce model A on the old production line? Explain.
g. Suppose that the minimum production requirement for model B is reduced from 70,000 units to 60,000 units. What effect would this change have on the total production cost? Explain.
Figure 3.21

Transcribed Image Text:

Minimum Production Requirements 50,000 70,000 Production Cost per Unit New Line $30 $25 80,000 Model Old Line $50 $40 60,000 Production Line Capacity Optimal Objective Value- 3850000.00000 Variable Value Reduced Cost AN AO BN BO 50000.00000 0.00000 30000.00000 40000.00000 0.00000 5.00000 0.00000 0.00000 Constraint Slack/Surplus Dual Value 1 0.00000 0.00000 0.00000 20000.00000 45.00000 40.00000 15.00000 0.00000 Objective Allowable Increase Allowable Decrease Variable Coefficient AO BN BO 30.00000 50.00000 25.00000 40.00000 5.00000 Infinite 15.00000 5.00000 Infinite 5.00000 5.00000 15.00000 RHS Allowable Increase Allowable Decrease Constraint Value 50000.00000 70000.00000 80000.00000 60000.00000 20000.00000 20000.00000 40000.00000 Infinite 40000.00000 40000.00000 20000.00000 20000.00000 4