A store owner estimates that by charging x dollars each for a certain lamp, he can sell 25 - x lamps each week. What price will yield maximum revenue?

Question

contestada

Respuesta :

yungsherman yungsherman · Answer 1 · 2019-07-31T10:32:53+02:00

Answer:

[tex]\frac{25}{2}[/tex] or 12.5

Step-by-step explanation:

So if 25 - x items are sold, and they each cost x, we can write an equation for the revenue to be

y = (25 - x)x

The vertex of this equation will represent the maximum revenue. So we need to write this equation in vertex form so we can find the vertex.

Vertex from is

y = a(x - h)^2+ k,

where (h,k) represent the vertex.

the vertex form of this equation would be

[tex]y= -(x-\frac{25}{2} )^{2} +\frac{625}{4}[/tex]

And the vertex would be

[tex](\frac{25}{2} ,\frac{625}{4})[/tex]

This means the maximum revenue will occur when x = 25/2

raphealnwobi raphealnwobi · Answer 2 · 2021-11-05T13:26:36+01:00

The maximum revenue is at a price of $11.5 each for a certain lamp

The revenue is the total amount of money that can be made from selling a number of goods.

Revenue = price * total number of items

Since the price per item is x dollars and the total number of items is 25 - x, hence:

Revenue (R) = x * (25 - x) = 25x - x²

R = 25x - x²

The maximum revenue is at dR/dx = 0, hence:

dR/dx = 25 - 2x

25 - 2x = 0

2x = 25

x = $11.5

Hence, The maximum revenue is at a price of $11.5 each for a certain lamp.

Find out more at: https://brainly.com/question/16872607