The Electrocomp Corporation manufactures two electrical products: air conditione

Question

The Electrocomp Corporation manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each fan must go through 2 hours of wiring and 1 hour o drilling. During the next production period, up to 240 hours of wiring time are available and up to 140 hours of drilling time may be used. In particular, management decides that to ensure an adequate supply of air conditioners for a contract, at least 10 air conditioners should be manufactured. Each air conditioner sold yields a profit of $25. Each fan assembled may be sold for a $15 profit. Formulate an LP Model to find the combination of air conditioners and fans. ( FORMULATION ONLY) The Electrocomp Corporation manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each fan must go through 2 hours of wiring and 1 hour o drilling. During the next production period, up to 240 hours of wiring time are available and up to 140 hours of drilling time may be used. In particular, management decides that to ensure an adequate supply of air conditioners for a contract, at least 10 air conditioners should be manufactured. Each air conditioner sold yields a profit of $25. Each fan assembled may be sold for a $15 profit. Formulate an LP Model to find the combination of air conditioners and fans. ( FORMULATION ONLY)

Explanation / Answer

Formulate the Problem

The given data is be summarized in following table

Air Conditioners

Large Fans

Minimum Required

Wiring Time (hours)

3

2

240

Drilling Time (hours)

2

1

140

Unit Profit($)

$25

$15

Decision Variables:

Let x1 be the number of Air conditioners to be produced

Let x2 be the number Fans to be produced

Objective Function:

Objective is to maximize the total profit by selling ACs and Fans. Unit profits both are $25 and $15 respectively. The profit function is given as follows:

Min. Z = $25x1 +$15x2

Production and Selling is subject to following constraints:

Thus, the mathematical equations for above constraints are as listed below:

3x1 + 2x2 <= 240

2x1 + x2 <= 140

x1 >= 10

x1, x2 0

Air Conditioners

Large Fans

Minimum Required

Wiring Time (hours)

3

2

240

Drilling Time (hours)

2

1

140

Unit Profit($)

$25

$15

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