Problem 2: Comp-Max Computers assembles computers and computer equipment. It is

Question

Problem 2: Comp-Max Computers assembles computers and computer equipment. It is about to start production of three new types of computers, called model X, Y, and Z, 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 400 hours, available inspection time is 300 hours, and available storage space is 500 cubic feet (about 14.2 m3). The amount of each resource required for the different products is reported in the table below. Model X earns a profit of $100 per unit, model Y earns a profit of $125 per unit, and model Z earns a profit of $200 per unit. Due to some prior agreements with customers, Comp-Max must produce at least 12 model X computers. In addition, management requires that the fraction of total production made up of model Z computers must not exceed 25% RESOURCE REQUIREMENTS Assembly time Inspection time Storage space (hrs./unit) MODEL hrs./unit 2. 4 6 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. [2 pts] c).Write out any constraints necessary for this problem in terms of the decision variables defined above. [10 pts]

Explanation / Answer

(a) THe decision variables are the unit of X, Y & Z to be produced.

(b) Here as we have to maximize the profit. Lets say we produce x, y & z unit of X , Y & Z respectivvely.

Let say total profit is TP, then we have to maximize

TP = 100X + 125Y + 200Z

(c) Here constraints are:

(i) Available assemply time:

6X + 7Y + 8Z   400 ..(i)

(ii) Avaialbele inspection time

X + 2Y + 3Z 300 ...(ii)

(iii) Avaialbe storge space

2X + 4Y + 6Z 500 ....(iii)

(iv) X 12

(v) Z 0.25 * ( X + Y + Z)

(vi) Y, Z 0

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