Comp-Max Computers assembles computers and computer equipment. It is about to st

Question

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 250 hours, available inspection time is 100 hours, and available storage space is 100 cubic feet (about 2.8 cubic meters). The amount of each resource required for the different products is reported in the table below. Model A earns a profit of $75 per unit, model B earns a profit of $65 per unit, and model C earns a profit of $55 per unit. Due to some prior agreements with customers, Comp-Max must produce at least 8 model A computers. In addition, management requires that the fraction of total production made up of model C computers must not exceed 20%. Comp-Max Computers assembles computers and compute Formulate a linear program (LP) that will help the manager determine the quantity of each model to produce in order to maximize profit. (Note: You do not have to solve the LP ? just formulate it!)

a.)Define the decision variables for this problem. [6 pts]

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

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

Explanation / Answer

Note: In the table, no units are mentioned. So, we have assumed Assembly time and Inspection time are in hours and space is in cubic feet.

(a)

Decision variables

Let A, B, C be the number of Model A, B, and C to be produced respectively.

(b)

Objective Function

Max.Z = Total profit = 75A + 65B + 55C

(c)

Constraints

Subject to,
10A + 7B + 5C 250 (Assembly hours availablity)
4A + 3B + 2C 100 (Inspection hours availability)
3A + 2B + 1C 100 (space availability)
A 8 (minimum qty of A)
0.8C - 0.2A - 0.2B 0 (restriction on model C)

A, B, C 0

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