Problema Solution
7. A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function R(x) = 80x - 2x^2 , where R is in dollars. What is the maximum revenue that can be generated?
Answer provided by our tutors
We need to find the maximum of the parabolic function R(x) = 80x - 2x^2
The quotient in front of x^2 is -2<0 thus the function has maximum.
R max = c - (b^2)/(4a)
a = -2, b = 80, c = 0
R max = 0 - (80^2)/(4*(-2))
R max = $800
The maximum revenue that can be generated is $800.