Davison Electronics manufactures two LCD television monitors, 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 obtained using The Management Scientist is shown in Figure.
THE MANAGEMENT SCIENTIST SOLUTION TO THE DAVISON ELECTRONICS PROBLEM

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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 the Management Scientist solution in Figure.
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 price is the constraint on the capacity of the new production line. The manager’s interpretation of the dual price 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 Aon 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.

Minimum Production Requirements 50,000 70,000 Production Cost per Unit Model New Line $30 $25 80,000 Old Line $50 $40 60,000 Production Line Capacity OPTIMAL SOLUTION Objective Function Value 3850000.000 Variable Value Reduced Costs AN AO BN 50000.000 0.000 30000.000 40000.000 0.000 5.000 0.000 0.000 Constreint Slack/Surplus Dual Prices 0.000 0.000 0.000 20000.000 -45.000 40.000 15.000 0.000 OBJECTIVE COEF1CIENT RANGES Variable Lower Limit Current Value Upper Linit AN AC BN BO 30.000 50.000 No Upper Limit 25.000 40.000 15.000 35.000 20.000 25.000 40.000 45.000 IGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Linit 10000.000 30000.000 60000.000 40000. 000 50000.000 70000.000 80000.000 60000.000 No Upper Linit 70000.000 90000.000 120000.000