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 what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y, equals, minus, 3, x, squared, plus, 104, x, minus, 423
y=−3x
2
+104x−423
Answer

Answer 1

The profit is maximized at the vertex of y = −3x^2 + 104x − 423. For ax^2+bx+c the vertex x = −b/(2a), so

x = −104/(2·(−3)) = 104/6 = 52/3 ≈ 17.3333.

To the nearest cent: $17.33 per widget.