Question

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar.
y, equals, minus, 5, x, squared, plus, 263, x, minus, 1844
y=−5x
2
+263x−1844
Answer

Answer 1

The parabola opens downward (a = −5), so the maximum occurs at the vertex x = −b/(2a) = −263/(2·−5) = 26.3.
Evaluate y at x = 26.3:

y = −5(26.3)^2 + 263(26.3) − 1844 = 1614.45 ≈ $1,614.

Maximum profit ≈ $1,614.