find out the maximum amount of profit the company can make, to the nearest dollar. y=-4x^2+183x-1247 y=−4x 2 +183x−1247

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,

Answer 1

y = -4x² + 183x - 1257

If you aren't taking calculus yet, then you need to recognize that this is a quadratic equation. Since the coefficient of the x² term is negative (-4), the parabola is inverted with its vertex at the top. The y-value of the vertex will be the maximum profit. The x-value of the vertex for a quadratic equation in standard form, y = ax² + bx + c, is:

x = -b/2a

In the profit equation, b = 183 and a = -4. Once you have the value of x for the vertex, plug it into the profit equation above to find the y-value (maximum profit). As stated in the instructions, round the profit to the nearest dollar.

Answer 2

y=-4x^2+183x-1247 y=−4x 2 +183x−1247

Taking the derivative and setting it = 0 yields the maximum value

0 = -8x + 183

8x = 183

x = $22.88 price for maximum profit

y(22.88) = 846.06 profit