Question

determine the maximum profit in the price that would yield the maximum profit for P=-400p^2+12,400p-50,000

Answer 1

To find the price which would yield the maximum profit we divide b by 2a as follows:

P$=-$ 400P$^{2}+$ 12400P $-$ 50000

$\frac{-b}{2a}=$ $\frac{-12400}{2(-400)}$

$=\frac{-12400}{-800}$

Answer is 15.50

To find the maximum profit we substitute this value of price in the profit equation as follows;

P$=-$ 400${(15.5}^2)$ $+$ 12400$($ 15.5$)$ $-50000$

$-$ 96100$+$ 192200$-$ 50000

Answer is 46 100

So the profit maximizing price is $15.50 and the maximum profit at this price is $46 100