Question

Digital Control manufactures two LCD television monitors, identified as model A and model B. Each model has its lowest production cost when produced on Davison’s new production line. However the new production line does not have 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 cost (in rand) per unit for each production line.

	Production cost/unit	Production cost/unit
Model	New Line	Old Line	Minimum requirement
A	R3 000	R5 000	50 000
B	R2 500	R4 000	70 000
Production Line Capacity	80 000	60 000

Model Production cost per unit Minimum production requirements New Line Old Line A R3 000 R5 000 50 000 B R2 500 R4 000 70 000 Production line capacity 80 000 60 000

Digital Control’s objective is to determine the minimum cost production plan.

Formulate the linear programming model for this problem. Clearly define the decision variables.

Answer 1

The linear programming model for this problem

Minimize 3,000AN + 5,000AO + 2,500BN + 4,000BO

Subject to

AN + AO >= 50,000

BN + BO >= 70,000

AN + BN <= 80,000

AO + BO <= 60,000

Decision variables are -

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