The total revenue for a commodity is given by R(x) = 2x √(500 - x) , when there is a demand for x units. The maximum total revenue is approximately:

Question

The total revenue for a commodity is given by R(x) = 2x √(500 - x) , when there is a demand for x units. The maximum total revenue is approximately:

Answer 1

Take the first derivative of the function and set it to zero and solve for x

d/dx (2x)( 500-x)^1/2= 2(500-x)^1/2 + (2x) ( -1/2) (500-x)^-1/2= 2(500-x)1/2 -x/(500-x)^1/2=

[2(500-x)^3/2 -x]/ (500-x)^1/2

set this to zero and solve for x = 333 1/3

when x= 333 1/3 y=8606

Answer 2

take the derivative and set it = 0, solve for x, then substitute back into the original equation

R(x) =2xsqr(500-x)