Anonymous

# can you please help with this question?

Carly has just opened her nail salon. Based on experience, she knows that her daily profit,P, in dollars, can be modeled by the relation P = −15x²+ 240x − 640, where x is the number of clients per day. How many clients should she book each day to maximize her profit?

### 2 Answers

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- alexLv 71 month ago
Rule:

P(x)=ax^2 + bx + c , with a<0---> maximum at x = -b/(2a)

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- Iggy RockoLv 71 month ago
P is at a maximum where P '(x) = 0 and P ''(x) < 0.

P '(x) = -30x + 240

0 = -30x + 240

x = 8

P ''(x) = -30 for all x so we know the maximum occurs at x = 8.

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