Question

A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function r(x) = 100x − 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:

Therefore the maximum revenue is $5,000 and 100 units should be manufactured to obtain the maximum revenue.

Explanation:

Given function is

r(x) = 100x- 0.5 x²

where the revenue r(x) is in dollar and no. unit is x.

We know that if function

y = ax²+bx+c.

Then we get the maximum value of y when $x= -\frac b{2a}$

Here a= -0.5 , b = 100 and c=0.

Therefore,

$x=-\frac{100}{2.(-0.5)} =100$

Therefore we get maximum revenue when x=100.

∴ r(100) = 100.100- 0.5(100)²

             =$5000

Therefore the maximum revenue is $5,000 and 100 units should be manufactured to obtain the maximum revenue.