CALCULATE OUTPUT MAKING MAXIMUM PROFITS

Question

You have been appointed as the Revenue Manager at Kabasorian Suppliers. From research, you have established that the company has an economic model that it uses to calculate their Revenues as well as their Costs. If the models are:

Total Revenue   R(X) = 2500-5X²                                                  

Total Cost C(X)= 40+3 X

Calculate the level of output that would make the company realize maximum profits.

Answer 1

Profit (P) equals Revenue (R) minus Cost (C):

P(x) = R(x) - C(x)

P(x) = (2500 - 5x²) - (40 + 3x)

P(x) = 2500 - 5x² - 40 - 3x

P(x) = -5x² - 3x + 2460

This is an upside-down parabola so it will have a maximum (which you are looking for). To find the maximum, take the derivative and set it equal to zero:

P'(x) = -10x - 3

Setting this equal to zero: -10x - 3 = 0 means x = -3/10

In this case, the maximum profit occurs when the company makes negative units. That's really strange. The more units the company makes, the less profit they make. Since they can't actually make negative units, then they should make zero units for which their profit is $2460.

Perhaps you made an error in transcribing the problem. If not, I suggest the company develop new models because to make nothing and still produce a profit sounds suspect.