The price demanded per x units of a good is 40 8x What is t

The price demanded per x units of a good is 40 - 8x. What is the total revenue when x units are sold, R(x)? For what values of x does the demand function p(x) = 40 - 8x from problem make sense?

Solution

Price demanded = 40 -8x

When x units are sold then, R(x) = x*( 40 -8x) = -8x^2 +40x

p(x) >=0 ; 40 -8x >=0

8x <= 40 ---> x<=5

But quantity demanded cannot be negative : so, x>=0

So, 0<= x<= 8

[ p(x) at x=0 ; p(0) = $ 40

p(15) = 40 -15*8 =- $80 which is not possible]