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)=800−0.4x is the unit price. Find the maxim

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)=800−0.4x is the unit price. Find the maximum revenue.

Answer 1

R(x) = x * (800 - 0.4x)

 

         = 800x - 0.4x^2

 

The max. occurs at the AVERAGE of the solutions.

The solutions are 0 = 800x - 0.4x^2

                         0  = 8000x - 4x^2

                         0 = 2000x - x^2

 

                         0 = x (2000 - x)

             

                        x=0 and 2000 - x = 0

                        x=0 and x =2000

 

 The average is 1000

 

Max Revenue is R(1000) = 1000* (800  - 0.4*1000)

                                    = 1000 * (800 - 400)

                                    = 1000 * (400)

 

                                    = 400000