Question

The revenue function for a bicycle shop is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x)=200−0.4x is the unit price. Find the maximum revenue.

Answer 1

maximum revenue is 25000

Explanation:

The revenue function for a bicycle shop is given by R(x)=x⋅p(x)

Given
`p(x)= 200-0.4x`

`R(x)=x \cdot p(x)`

Plug in p(x) in R(x)

`R(x)=x \cdot 200-0.4x`

`R(x)=200x-0.4x^2`

Now find out the vertex using formula x=-b/2a

a= -0.4, b=200

`x=(-b)/(2a) =(-200)/(2(-.4)) =250`

Plug in 250 for x in R(x)

`R(x)=200x-0.4x^2`

`R(x)=200(250)-0.4(250)^2=25000`

So maximum revenue is 25000