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?

Answer 1

Answer: maximum revenue is 1800. 60 units need to be manufactured to obtain the maxim.

Step-by-step explanation:

Maximum is the y-value of the vertex.  The number of units at the maximum is the x-value of the vertex.

R(x) = 60x - 0.5x²   ⇒   R(x) = -0.5x² + 60x ⇒ a = -0.5, b = 60, c = 0

Axis of Symmetry: x = $\frac{-(b)}{2(a)}$ = $\frac{-(60)}{2(-0.5)}$ = $\frac{-60}{-1}$ = 60

Plug the x-value into the given equation to find the y-value of the vertex:

R(60) = -0.5(60)² + 60(60)

         =   -1800   +   3600

         =             1800

Vertex: (60, 1800)