the question was too long so its in the description

Question

The profit of a designer bag company is represented by the function y=-2x^2+100x+60 , where x represents the cost of the designer bag. What price should the company charge per bag to maximize its profit? What is the maximum profit?

Answer 1

Hello, Athena,

The equation y=-2x²+100x+60 is a parabola. What you want is the highest point on that parabola, where y (the profit) is highest. x (the price of one designer bag) will be the point where the curve stops going up and starts heading down. The slope of the line at this point is zero.

We can find the optimum price in one of two ways:

A. Graph it. Then find the value of x where the parabola peaks:

B. Obtain the first derivative and set it to 0, the slope at the highest point:

y=-2x²+100x+60

dy/dx = -4x +100

0 = -4x + 100

x = 25

$25 is the price that will bring the highest income.

The total revenue would be -2(25)² + 100(25) +60 = $1,310

Bob

Bob