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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 Davisonâ€™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

Davisonâ€™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

.

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 managerâ€™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.

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