A business man has determined that a mathematical model for his profit(in thousands of dollars) from the sales of a commodity at price x dollars is p(x)=-x^2+20x-50.

a) for what price is his profit maximized?

b) what is his maximum profit

(a) the equarion is that of a parabola. In a parabola the maximum occurs at vertex.

The vertex of a parabola is given as

therefore the price for which the profit is maximized is $10

(b) the maximum profit is given as $50

Feel free to ask any doubts

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