Question

RUSH RUSH Decision making technics.. A company uses two machines (Machine 1 and Machine 2) to produce product A. Each hour of operation, Machine 1 produces 50 products and Machine 2 produces 75. It cost the company $250/hour, and $325/hour to operate Machine 1 and Machine 2, respectively. Machine 2 has to produce at least 30% of all products. If the two machines [together] must produce at least 500 products each day and each machine can run for at most 8 hours a day, in one paragraph, discuss: 1.What are the decision variables (include the values they can take), restrictions, and the objective function of the problem?

Answer 1

Hello

Let X be the number of hours Machine 1 works.

Let Y be the number of hours Machine 2 works.

Then,

1. The decision Variables are X & Y,i.e. the number of hours each machine should operate in order to minimize cost, given restrictions.

2. Restrictions:

50X + 75Y 500

75Y   0.3*(50X + 75Y)

X 8

Y 8

3. Objective function refers to the function whose value is targeted to be minimized/ maximized.

Hence, objective function, z, here is the cost function, which tells about the costs of running both machines.

z = 250*X + 325*Y

I hope this solves your query.

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