To start production jof three new types of computers, called A, B, and C. Each t

Question

To start production jof three new types of computers, called A, B, and C. Each type will require assembly time, insepction time, and storage space. The availability of each of these resources is limited. Specifically, available assembly time is 440 hours, available inspection time is 90 hours, and available storrage space is 156 cubic feet. The amount of each resource required for the differenct produccts 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 with customers, must produce at least 10 model A computers. In addition, management requires that the fraction of total production made up of model C, computes must not exceed 25%. Formultate a linear program(LP) that will help the manager determine the quality of each model to produce in order to maximize profit. Q1) define the decision variable for this problem. Q2) write out the object function fro this problem in terms of the decision variables define above. Q3) write out any constraints necessary for this problem in terms of the decision variables defined abouve.

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

Explanation / Answer

Q1)

Decision variables:

Let A = No of model A

B = no of model B

C = no of model C

(Q2)

Objective Function is to maximize the profits

Max Z = Total profit = 160A + 120B + 90C

Q3)

Constraints:

Subject to

16A + 8B + 20C ? 440 (Assembly hours availability)

8A + 4B + 2C ? 90 (Inspection hours availability)

4A + 6B + 8C ? 156 (space availability)

A ? 10 (minimum quantity of A)

0.75C - 0.25A - 0.25B ? 0 (restriction on model C)

A, B, C ? 0

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