SOLUTION: A chain store manager has been told by the main office that daily profit, P, is related to the number of clerks working that day, x, according to the equation P= -25x^2 + 300x. Wh

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Question 154503: A chain store manager has been told by the main office that daily profit, P, is related to the number of clerks working that day, x, according to the equation P= -25x^2 + 300x. What number of clerks will maximize the profit, and what is the maximum possible profit?
Answer by BrittanyM(80) About Me  (Show Source):
You can put this solution on YOUR website!
In order to find the point at whiich profit is maximized, we must find the critical points of the first derivative of the equation.

P = -25 x%5E2 + 300x

The first derivative is

0 = -50x + 300

And solving,

x = 6

So six clerks will optimize profits. In order to find the profits at this point, we can plug our value of x back into the original equation.

P = -25%286%29%5E2+%2B+300%286%29

P = -900 + 1800

So we know that at six clerks, Profit runs at $900