Linear programming graphing

B7.

The Attaran Corporation manufactures two electrical

products: portable air conditioners and portable heaters. 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 heater must go through

2 hours of wiring and 1 hour of drilling. During the next production

period, 240 hours of wiring time are available and up to

140 hours of drilling time may be used. Each air conditioner sold

yields a profit of $25. Each heater assembled may be sold for a

$15 profit.

Formulate and solve this LP production-mix situation, and

find the best combination of air conditioners and heaters that

yields the highest profit.

ANSWER:

Let x1 number of air conditioners to be produced

x2 number of heaters to be produced

Maximize 25x1  15x2

Subject to 3x1  2x2 240 (wiring)

2x1  1x2 140 (drilling)

x1, x2 0 (non-negativity)

Profit:

@a: (x1  0, x2  0)  Obj  $0

@b: (x1  0, x2  120) Obj  25  0  15  120  $1,800

@c: (x1  40, x2  60) Obj  25  40  15  60  $1,900*

@d: (x1  70, x2  0) Obj  25  70  15  0  $1,750

* The optimal solution is to produce 40 air conditioners and 60 heaters each period. Profit will be $1,900.