Answer to Question #244979 in Financial Math for Gavin

Question

Using the profit function,  p(x)=-900p^2+22,100p-100,000 find the price per unit at which the maximum profit is obtained.

Answer 1

The profit function is given by 

    p(x)= -900 p²+22,100p -100,000

We have to find p'(x)

    p'(x)= -1800p + 22,100

Putting p'(x) = 0

    -1800 p + 22,100 = 0

            -1800 p = - 22,100

$p= \frac{−22,100}{− 1800}=12.28$

Now, p"(x) = -1800

Since p"(x) <

< 0

     p = 12.28

Therefore maximum profit = p (12.28)

     p(x) = -900 p²+22,100p -100,000

  p(12.28) = -900(12.28)² +22,100 (12.28) -100,000

          = 35669.44

Hence the maximum profit is 35669.44 unit