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: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 x²where the revenue r(x) is in dollar and no. unit is x.We know that if functiony = ax²+bx+c.Then we get the maximum value of y when [tex]x= -\frac b{2a}[/tex]Here a= -0.5 , b = 100 and c=0.Therefore,[tex]x=-\frac{100}{2.(-0.5)} =100[/tex]Therefore we get maximum revenue when x=100.∴ r(100) = 100.100- 0.5(100)²              =$5000Therefore the maximum revenue is $5,000 and 100 units should be manufactured to obtain the maximum revenue.