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.

Question

Koba

Mathematics

30 December, 10:29

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.

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Answers (1)

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Tanner · Answer 1

x = 50

R = $2500

Step-by-step 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