Question 1059622: The function y = −x2 + 24x represents a model of the daily profit y in dollars earned by a restaurant when x people dine there for a day.
a. How many people need to eat there in order for the profit to be at least $80? Show your work.
b. How many people need to eat there in order for the profit to be more than $108?
c. Is it possible for the restaurant to lose money (make a negative profit) for a day? Explain.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! -x^2+24x=80
-x^2+24x-80=0
x^2-24x+80=0
(x-20)(x-4)=0, x=4 and 20, at least 4 and no more than 20 ANSWER a.
x^2-24x-108=0 (want to be more than that) (x-18)(x-6)=0.
x=6, 18. That is to be exactly 108, so the answer is between 7 and 17 inclusive ANSWER b.
Yes, with enough people, more than 24, the restaurant will lose money, ANSWER c.
x^2-24x=0, x(x-24)=0, and at 0 and 24, the restaurant will break even.
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