Question

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?

Answer 1

Answer:

$\frac{25}{2}$ 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

$y= -(x-\frac{25}{2} )^{2} +\frac{625}{4}$

And the vertex would be

$(\frac{25}{2} ,\frac{625}{4})$

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