The Saturn Company makes refrigerators and air conditioners. Two plants, I and I

Question

The Saturn Company makes refrigerators and air conditioners. Two plants, I and II, are used. The assembly work is done in plant I, and it is estimated that 5 labor-hours of work are required to produce a refrigerator and 2 labor- hours of work are required to produce an air- conditioner. The finishing work is done in plant II, and it is estimated that 3 labor-hours of work are needed to finish a refrigerator and 2 labor-hours are needed to finish an air-conditioner. Plant I has 220 labor-hours per week available and plant II has 180 labor-hours per week available. A market survey indicates that there is an unlimited market for these products.

If the Saturn Company makes a profit if $50 on each refrigerator and $30 on each air-conditioner, how many of each should be produced weekly so as to maximize profit?

(SET UP ONLY)

Explanation / Answer

Let x be the number of refrigerator produced and y be the number of air-conditioner produced.

Objective is to maximize the profit.

profit from a refrigerator = $50

profit from a air-conditioner = $30

So, Total profit = 50 x + 30 y

Plant I and Plant II are the resources available.

each refrigerator requires 5 hours of labour in Plant I and each air-conditioner requires 2 hours of labour in Plant I.

Plant I has a maximum of 220 labour-hours available per week.

Thus we get,

5 x + 2 y <= 220

each refrigerator requires 3 hours of labour in Plant II and each air-conditioner requires 2 hours of labour in Plant II.

Plant II has a maximum of 180 labour-hours available per week.

Thus we get,

3 x + 2 y <= 180

So the Linear program for this problem is;

Maximize 50 x + 30 y

subjected to

5 x + 2 y <= 220

3 x + 2 y <= 180

x , y >= 0

Thank you..   

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