Question

A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function R(x) = 80x − 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?
$ _______, at ______units

Answer 1

Given data in the question is as follows:

R(x)=80x-0.5x2

R(x)=-0.5x2 +80x

This is in the form of y=ax2+bx+c, for which the maximum value occurs at

where a=-0.5 and b=80

Pluggind a and b values in the above formula,

we get

So,at x=80 units , we will get the maximum revenue.

Mximum revenue =R(x=80)

=80x-0.5x2    (Plug x=80)

=80*80-0.5(80)2

   =6400-0.5*6400

   =3200

So Maxmimum revenue= $320

Maximum revenue = $3200

Maximum revenue occurs at x=80 units