Revenue = Demand x Price, p(x) = 150 - x over 4

[hanna]

I need your help getting started on this problem:

The manager of a bicycle shop has found that, at a price of p(x) = 150 - x over 4 per bicycle, x bicycle will be sold.
a) Find an expression for the total revenue from sale of x bicycle (revenue = demand x price).
b) Find the number of bicyle sales that leads to maximum revenue
c) Find the maximum revenue.

Thanks for your help, I am stuck.
hanna

 

[stapel]

The manager of a bicycle shop has found that, at a price of p(x) = 150 - x over 4 per bicycle, x bicycle will be sold.
a) Find an expression for the total revenue from sale of x bicycle (revenue = demand x price).

How is "demand" defined? If it is "the number sold at a given price", then wouldn't "revenue" be the product of the price function and the number sold?

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

Take the derivative. Find the maximizing value of x. (Or else just find the vertex of the parabola, like you did back in algebra.)

c) Find the maximum revenue.

Plug the maximizing value of x into the "revenue" function. Simplify to find the maximum revenue value.

If you get stuck, please reply showing all of your work and reasoning so far. Thank you!