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=-10x^2+600x-3588
y=−10x
2
+600x−3588

Step-by-step explanation:

The maximum profit will be found in the vertex of the parabola, which is what your equation is. You could do this by completing the square, but it is way easier to just solve for h and k using the following formulas:

for the x coordinate of the vertex, and

for the y coordinate of the vertex.

x will be the selling price of each widget and y will be the profit. Usually, x is the number of the items sold, but I'm going off your info here for what the vertex means in the context of this problem.

Our variables for the quadratic are as follows:

a = -10

b = 600

c = -3588. Therefore,

so the cost of each widget is $30. Now for the profit:

This one is worth the simplification step by step:

and

k = -3588 - (-9000) and

k = -3588 + 9000 so

k = 5412

That means that the profit made by selling the widgets at $30 apiece is $5412.