B.7 The Electrocomp Corporation manufactures two electrical products: air condit

ID: 2688747 • Letter: B

Question

B.7 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 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 fan 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 fans that yields the highest profit.

Explanation / Answer

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 of drilling. During the next production period, 240 hours of wiring time are available and up to 140 hours of drilling time maybe used. Each air conditioner sold yields a profit of $25.

Each fan assembled may be sold for a $15 profit. Formulate and solve this LP production mix situation to find the best combination of air conditioners and fans that yields the highest profit. Use the corner point graphical approach.

Let X1 = the number of air conditioners scheduled to be produced

X2 = the number of fans scheduled to be produced

Maximize

25X1

15X2

(maximize profit)

Subject to:

3X1

2X2

240

(wiring capacity constraint)

2X1

140

(drilling capacity constraint)

X1, X2

(non-negativity constraints)

Optimal Solution: X1 = 40 X2 = 60

Profit = $1,900