Amanufacturer 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. 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 = = = = 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)