## The Chocolate Company

Cost price of (10-x) chocolates:

(10x). 0.20 = 2 - 0.20x

Selling price of (10-x) chocolates:

(10x). x = 10x - x^{2}

Profit on (10-x) chocolates:

L (x) = (10x - x^{2}) - (2 - 0.20x)

L (x) = 10x - x^{2} - 2 + 0.20x

L (x) = -x^{2} + 10.20x -2

Deriving we have:

L '(x) = -2x + 10.20

L '(x) = 0 => -2x + 10.20 = 0 => **x = 5.10**

Answer: The price of chocolate at $ 5.10 maximizes the company's profit.

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