Linear Regression The Electrocomp Corporation manufactures two electrical produc

Question

Linear Regression

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 to find the best combination of air conditioners and fans that yields the highest profit.

Explanation / Answer

To formulate, we need to define the variables as follows:

Let X1 be the number of air conditioners to be produced and X2 be the number of fans to be produced.

The maximum profit can be achieved at the following level of output (the equation)

Maximum Profit = 25*X1 + 15*X2

which would be subject to following constraints:

3*X1 + 2*X2<= 240 (wiring)

2*X1 + 1*X2<= 140 (drilling)

Using the equation for drilling, we derive,

X1 = (140 - X2)/2 = 70 - .5*X2

Substituting this value of X2 in the equation for wiring capacity constraint, we get,

3*(70 - .5*X2) + 2*X2 = 240

Rearranging Values, we get,

X2 = (240 - 210)/(-1.5 + 2) = 60 units of fans will be produced

Based on this, we can derive the number of air conditioners that would be produced as follows:

X1 = 70 - .5*60 = 40 units of air conditioners will be produced

___________

Maximum Profit that can be achieved with these units is calculated as follows:

Maximum Profit = 25*40 + 15*60 = $1,900

___________

Optimal Solution (Answer)

40 units of air conditioner, 60 units of fan and $1,900 maximum profit

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