To determine whether to purchase a company's stock, an investor will use a profit-prediction formula for a company's signature product depending on that product’s current selling price. The profit formula for the company can be represented using the function P(x)=−20x^2+4,400x−24,000 , where x is the selling price of the product. Use a graphing calculator to determine the selling price that results in the maximum profits. Round to the nearest cent if necessary.
The profit function is a downward-opening quadratic because the coefficient of x² is −20, so its maximum occurs at the vertex. The vertex’s x-coordinate is −b/(2a) = −4,400/(2 × −20) = 110, so the selling price that gives the maximum profit is 110 dollars.
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