Question

Laura owns and operates aunt linda's pecan pies. she has learned that the profits, p(x), from the scale of x cases of pies, are given by p(x) =150x-x^2
a.) the company will "break-even" when the profit is zero. how many cases of pies should laura sell in order to break- even?
b.) how many cases of pies should she sell in order to maximize profit?
c.) what is the maximize profit? please show work! - thank you so much!!

Answer 1

0 = 150x - x^2
x(150 - x) = 0
150 - x = 0
x = 0 or x = 150
Therefore, she need to sell 150 cases to break even.

At maximum profit, p'(x) = 150 - 2x = 0
2x = 150
x = 150/2 = 75
To maximize profit she should sell 75 cases .\

Maximum profit = 150(75) - (75)^2 = 11250 - 5625 = 5,625