have problem solving this

Question

A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function R(x) = 60x − 0.2x2, 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?

Answer 1

60x - .2x^2 = total Revenue = R(x) = R

take the derivative and set = 0, solve for x

R' = 60 - 4x = 0

x = 60/.4 = 600/4 = 150

plug 150 for x into R(x)

= R(150) = 60(150) -.2(150)^2 = 9000-22500/5

= 9000- 4500=$4500= max revenue

need to manufacture 150 units

that's the differential calculus method

or use algebra and find the vertex of the parabola

or graph it and find the max point (150, 4500)

calculus, algebra, graph, your choice

Answer 2

Maximum revenue is at the vertex.

Transform into vertex from (from Algebra 2)