bikehelmet.net

x bicycles will be sold.

a) Find an expression for the total revenue from the sale of x bicycles. (Hint: revenue = demand x price)

b) Find the number of bicycle sales that leads to maximum revenue.

c) Find the maximum revenue.

Tagged with: Bicycle • bicycle sales • bicycle shop • bicycles • expression • Hint • manager • maximum • maximum revenue • number • price • revenue • sale • shop

[^2 denotes to the power of 2, or squared in other words]

Price = 150 - x/4

Demand = x

Revenue = demand x price

Revenue = x(150 - x/4)

Revenue = 150x - x^2/4

Stationary points (maximum/minimum points) occur when R' = 0

R = 150x - x^2/4

R' = 150 - 2x/4

R' = 150 - x/2

when R' = 0

0 = 150 - x/2

x/2 = 150

x = 300 (stationary point - assume maximum as only one point exists)

Use revenue equation to find revenue at maximum point:

R = 150(300) - 300^2/4

R = 45000 - 22500

R = $22,500