Electro Corp. Co. manufactures two electrical products :Air conditioners and Fans. The assembly process for each is similar in which both require a certain amount of wiring and drilling. Each air conditioner takes 4 hours for wiring and 2 hours for drilling. Each fan also takes 2 hours for wiring and 1 hour for drilling. During the next production period, 240 hours of wiring time are available and upto 100 hours of drilling time may be used. Each air-conditioner assembled may be sold for Rs. 2,000 profit and each fan assembled may be sold for Rs. 1,000 profit. Formulate this problem as an L.P.P. in order to maximize the profit.

#### Solution

Air conditioner | Fans | Available hrs. | |

x | y | ||

Wiring | 4 | 2 | 240 |

Drilling | 2 | 1 | 100 |

Let x = number of airconditioners

y = number of fans

4x + 2y ≤ 240

2x + y ≤ 100

Since the number ofair conditioners and fans cannot be negative.

x ≥ 0, y ≥ 0

The objective function to be maximised is

x = 2000x + 1000y

The L.P.P is:

Maximize profit Z = 2000x + 1000y

Subject to 4x + 2y ≤ 240

2x + y ≤ 100

x ≥ 0, y ≥ 0

Where x = number of air conditioners,

y = number of fans.