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, 103, x, minus, 980
y=−x
2
+103x−980
To find the price at which the company should sell the widgets in order to maximize profit, we need to find the vertex of the parabolic equation y = -x^2 + 103x - 980.
The x-coordinate of the vertex of a parabolic equation in the form y = ax^2 + bx + c is given by x = -b/2a. In this case, a = -1 and b = 103.
x = -103 / 2(-1)
x = 103 / 2
x = 51.5
Now that we have found the x-coordinate of the vertex, we can substitute this back into the equation to find the maximum profit:
y = -(51.5)^2 + 103(51.5) - 980
y ≈ -$267.25
Therefore, in order to maximize profit, the widgets should be sold for $51.50.