R(x) = 60x − 0.5x^2, What is the maximum revenue, and how many units should be manufactured to obtain this maximum?

Question

A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function R(x) = 60x − 0.5x², where the revenue R(x) is measured in dollars. What is the maximum revenue, and how many units should be manufactured to obtain this maximum?

Maximum revenue is $1800. I am trying to solve: "How many units should be manufactured to obtain this maximum?" _____ units

Thank you.

Answer 1

R = 60x - 0.5x^2

take the derivative and set equal to zero, then solve for x to get the revenue maximizing output level

R' = 60 -x = 0

x = 60, plug that value into the R(x) equation

R=60(60) - 0.5(60)^2 = 3600-1800 = $1800 = max revenue when output = 60 units