Problem 4: Comp-Max Computers assembles computers and computer equipment. It is about to start production of three new types of computers, called model A, B, and C, respectively. Each type will require assembly time, inspection time, and storage space. The availability of each of these resources is limited. Specifically, available assembly time is 200 hours, available inspection time is 44 hours, and available storage space is 78 cubic feet (about 2.2 m3). The amount of each resource required for the different products is reported in the table below. Model A earns a profit of $80 per unit, model B earns a profit of $60 per unit, and model C earns a profit of $45 per unit. Due to some prior agreements with customers, Comp-Max must produce at least 5 model A computers. In addition, management requires that the fraction of total production made up of model C computers must not exceed 25%.

Formulate a linear program (LP) that will help the manager determine the quantity of each model to produce in order to maximize profit.

a). Define the decision variables for this problem.

b). Write out the objective function for this problem in terms of the decision variables defined above.

c). Write out any constraints necessary for this problem in terms of the decision variables defined above