Question

A retailer who sells backpacks estimates that by selling them for x dollars each, she will be able to sell 100−x backpacks each month. The quadratic function R(x)=−x2+100x is used to find the revenue, R, received when the selling price of a backpack is x. Find the selling price that will give her the maximum revenue, and then find the amount of the maximum revenue.

Answer 1

x = 50

R = $2500

Explanation:

Given in the question a quadratic equation,

−x² + 100x

To find the selling price, x, which will give highest revenue, y, we will find maximum value of parabola curve −x² + 100x

The value of -b/2a tells you the value x of the vertex of the function

−x² + 100x

here a = -1

b = 100

Selling price = -(100)/2(-1)

= 50

R = −(50)² + 100(50)

= 2500