Question

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

​$20

Each heater assembled may be sold for a

​$15

profit.

The optimum solution​ is:

Number of air conditioners to be produced​ =

0

​(round your response to two decimal​ places).

Number of heaters to be produced​ =

nothing

​(round your response to two decimal​ places).

Answer 1

The problem is linear programming problem with objective is to maximize profit:

Objective function : Maximize Z = 20X₁ + 15X₂

Here,

• 20 is per unit profit from air conditioner and X₁ is the no. of air conditioners to be produced
• 15 is per unit profit from heater and X₂ is the no. of heaters to be produced

Subject to:

3X₁ + 2X₂ 240 (Total wiring time available)

2X₁ + 1X₂ 140 (Total drilling time available)

X₁ and X₂ 0 (Non negativity)

The excel formulation is shown below:

The solver equations are shown below:

The solution is shown below:

The product mix is shown below:

• 0 units of Air conditioners should be manufactured
• 120 units of heaters to be manufactured

The total profit is $1800