Question

Laura owns and operates Aunt Linda’s Pecan Pies. She has learned that her profits, P(x), from the sale of x cases of pies, are given by P(x) = 150x – x2.
a. The company will “break-even” when the profit is zero. How many cases of pies should Laura sell in order to break-even? (Solve for x when P(x) = 0.) Write your answer in a complete sentence with proper grammar and correct spelling.


b. How many cases of pies should she sell in order to maximize profit? What is the maximum profit? Write your answer in a complete sentence with proper grammar and correct spelling.

Answer 1

Step-by-step explanation:

Part a

P(x) = 0

150x - x^2 = 0

x(150-x)

x=0,150

Laura should sell 150 pies in order to "break-even" on her sales.

Part b

Because the maximum profit occurs at the vertex of the function,

x = -b/2a = -150/-2 = 75

P(75) = 150 * 75 - 75^2 = 5625

Laura maximizes her profit to $5625 when she sells exactly 75 pies.