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, x, squared, plus, 90, x, minus, 594
y=−x
2
+90x−594
To find the maximum profit, we can use the vertex formula for a quadratic equation in the form y = ax^2 + bx + c. The x-coordinate of the vertex of the parabola represented by the equation is given by the formula x = -b/2a.
In this case, a = -1, b = 90, and c = -594.
x = -90 / (2*(-1))
x = -90 / -2
x = 45
Therefore, the widgets should be sold for $45 to maximize profit.