SOLUTION: GoQuik Dinners makes meals for people on the go. The company models their profit with the function P = -2x^2 + 14x - 20, where x is the number of meals produced in hundreds, and P

Question 1032512: GoQuik Dinners makes meals for people on the go. The company models their profit with the function P = -2x^2 + 14x - 20, where x is the number of meals produced in hundreds, and P is the company's profits, in thousands
a) How many meals must be produced for the company to break even?
b) How many meals does GoQuik need to produce to maximize their profit?
c) What is the maximum profit they could earn?
Thanks
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
a) To break even, P = 0...we get

Thus they break even at 200 meals and at 500 meals.
b) To maximize profit, we take the derivative and set it equal to zero, so that
P' = -4x + 14 = 0
and
x = 3.5 = 350 meals
c) To find out what that profit is, we plug 3.5 in for x in the original and get
P(3.5) = -2(3.5)^2 + 14(3.5) - 20 = 4.5 = $4500
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