Use the format

(i) Define the decision variables

(ii) State the objective function

(iii) State the constraints

Each of these steps carry points.

1. Procomp Inc. produces two types of computers, the SX and the EX. They have two production departments, Assembly and Packaging. In Assembly department, each SX computer requires 0.4 labor hour and an EX requires 0 .5 labor hours. Presently, in Assembly department, a maximum of 360 labor hours per week can be assigned to the production of the two types of computers. In Packaging department, an SX requires 0.1 labor hour and an EX requires 0.15 labor hour. Presently, Packaging department has a maximum of 120 labor hours per week that can be assigned to the two computer models. In order to maintain the current market position, top management has issued a policy that it is necessary to build at least 250 EX computer. Procomp already has a backorder of at least 30 SX computers it promised to deliver to a major customer. The profit contributions are $10 and $20 respectively for each SX and each EX set.

Question

If the marketing manager at Procomp has determined that they can sell as many computers as they can produce, formulate a linear programming model that can be used to determine the optimal number of each type of computer to produce in order to maximize profit.