Question

Davison Electronics manufactures two LCD television monitors, identified as model A andmodel B. Each model has its lowest possible production cost when produced on Davison’snew production line. However, the new production line does not have the capacity to han-dle the total production of both models. As a result, at least some of the production mustbe routed to a higher-cost, old production line. The following table shows the minimumproduction requirements for next month, the production line capacities in units per month,and the production cost per unit for each production line:

Answer 1

The question is incomplete. The complete question is :

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:

                      Production per unit                         Minimum production

Model        New Line        Old Line                              requirements

A                   $30                $50                                          50,000

B                   $25                $40                                           70,000

Production  80000          60000

line capacity.

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  

Solution :

Linear programming model:

Linear programming is defined as a mathematical model where the linear function is either minimize or maximize when they are subjected to some constraints.

The linear programming model is determined as follows :

Minimum : 30 AN + 50 AO + 25 BN + 40 BO

This is subject to the constraints as :

$AN+AO \geq 60,000$

$BN+BO \geq 70,000$

$AN+BN \leq 80,000$

$AO+BO \leq 60,000$

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