Question

The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt. If the price is too high, sales will drop. If the price is too low, the revenue brought in may not cover the cost to produce the shirts. After months of data collected, the sales te determines that the monthly profit is approximated by f(p)= -50p^2+1700p-12000, where p is the price per shirt and f(p) is the monthly profit on that price. A) Find the price that generates the maximum profit B) Find the maximum profit C) Find the price(s) that would enable the company to break even.

Answer 1

Below

Explanation:

You could just graph the equation for the answers....

Here is algebraic method

for Quadratic Equation - 50p^2 +1700p - 12000

the max profit occurs at p = - b/2a = - 1700 / (2* -50) = 17 dollars

A ) 17 dollars

B) use p =17 in the equation to find profit = 2450 dollars

C) Set the equation = 0 and solve for p

0 = -50p^2+1700p - 12 000

Use Quadratic Formula with a = -50 b = 1700 c = 12000

to find price = 40 dollars