1. An air conditioning company manufactures three home air conditioners: model A

Question

1. An air conditioning company manufactures three home air conditioners: model A, model A+ and model A++. The profits per unit are $70, $100, and $145, respectively. The production requirements per unit and the availability of the three resources are given below:

Model A

Model A+

Model A++

Available

Number of fans

1

1

1

400

Number of cooling coils

2

2

4

600

Manufacturing Time

12

16

20

4500 hours

How many model A, model A+ and model A++ air conditioners should the company manufacture in order to maximize profit?

2. Find the computer solution, including the ranging (sensitivity analysis) results, for Question 1 by using QM for Windows or Excel. Determine the optimal solution (including the decision variables and the slack/surplus variables) and optimal profit. Interpret the optimal solution and optimal profit.

Model A

Model A+

Model A++

Available

Number of fans

1

1

1

400

Number of cooling coils

2

2

4

600

Manufacturing Time

12

16

20

4500 hours

Explanation / Answer

Let x be the number of Model A, y be the number of Model A+ and z be the number of Model A++ to be manufactured in order to maximize the profit

Maximize Profit = 70x + 100y + 145z
subject to,
x + y + z <= 400 (Constraint of number of fans)
2x + 2y + 4z <= 600 (Constraint of number of coils)
12x + 16y + 20z <= 4500 (Constraint of time)

Hence Maximum profit of $28625 can be earned when below number of models will be manufactured,

Model A - 0

Model A+ - 250

Model A++ - 25

Solver Solution x y z Total Supply Decision Variables 0 250 25 Profit 70 100 145 28625 Constraint 1 1 1 1 275 400 Constraint 2 2 2 4 600 600 Constraint 3 12 16 20 4500 4500

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