Question

The price p (in dollars) and the quantity x sold of a certain product obey the demand equation:

x = -20p + 500 where 0 < p ≤ 25
Revenue, R, can be found by the following equation: R = xp. Express R as a function of x hellppp?

Answer 1

x = - 20 p + 500
First we have to express p as a function of x:
20 p = - x + 500 / : 20
p = - x/20 + 25
The revenue:
R = x p
R = x ( - x/20 + 25 ) = - x²/20 + 25 x

Answer 2

x = -20p + 500
20p = 500 - x
p = (500 - x)/20

R = xp = x(500 - x)/20 = (500x - x^2)/20