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=-x^2+51x-201

Answer 1

, the company should sell the widgets at a price of approximately $25.50 (rounded to the nearest cent) in order to maximize profit.

Explanation:

To find the price at which the company should sell the widgets to maximize profit, we need to determine the vertex of the quadratic equation y = -x^2 + 51x - 201. The x-coordinate of the vertex represents the price that will yield the maximum profit.

The equation is in the form y = ax^2 + bx + c, where:

a = -1

b = 51

c = -201

The x-coordinate of the vertex can be found using the formula: x = -b / (2a)

Plugging in the values, we have:

x = -51 / (2 * -1) = -51 / -2 = 25.5