It is about to startt production of three new types of computers, called model A

Question

It is about to startt production of three new types of computers, called model A, B and C. Each type will require assembly time, insepction time, and storage space. The availability of each resources is limited. Specifically, available assembly time is 440 hrs, available inspection time is 90 hours, and available storage space is 156 cubic feet. The amount of each resources required for the different products is reported in the table below. Model A earns a profit of $ 160 per unit, model B earns a profit of $120 per unit, and model C earns a profit of $90 per unit. Due to some prior agreements which customers, the company must produce at least 10 model A computers. In additon, management requires that the fraction of total production made up oof model C comutere must not exceed 25%. Q1) define the decision variables for this problem. Q2) write out the objective function for this problem in terms of the decision variables define abouve. Q3) write out any constraints necessary for this problem in terms of the decision variables defined above.

model assmbly time(hrs./unit) inspection time(hrs./unit) storage space(cu.ft/time) A 16 8 4 B 8 4 6 C 20 2 8

Explanation / Answer

1) Decision variables: Let X1, X2, X3 be the optimal production quantity of each of the models A, B, C respectively

2) Objective: Max 160X1+120X2+90X3  (profit maximization)

3) Constraints:

16X1+8X2+20X3 <= 440

8X1+4X2+2X3 <= 90

4X1+6X2+8X3 <= 156

X1 >= 10

X3 <= 0.25*(X1+X2+X3) or, -0.25X1-0.25X2+0.75X3 <= 0

X1, X2, X3 >= 0

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