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

Answer:

maximum revenue is 25000

Step-by-step 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

$x=\frac{-b}{2a} =\frac{-200}{2(-.4)} =250$

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