A company’s total revenue from manufacturing and selling x units of their product is given by: y = –3x2 + 900x – 5,000. How many units should be sold in order to maximize revenue, and what is the maximum revenue

Answer:150 units; Maximum revenue: $62,500.Step-by-step explanation:We have been given that a company’s total revenue from manufacturing and selling x units of their product is given by [tex]y=-3x^2+900x-5,000[/tex]. We are asked to find the number of units sold that will maximize the revenue.We can see that our given equation in a downward opening parabola as leading coefficient is negative.We also know that maximum point of a downward opening parabola is ts vertex.To find the number of units sold to maximize the revenue, we need to figure our x-coordinate of vertex.We will use formula [tex]\frac{-b}{2a}[/tex] to find x-coordinate of vertex.[tex]\frac{-900}{2(-3)}[/tex] [tex]\frac{-900}{-6}[/tex] [tex]150[/tex] Therefore, 150 units should be sold in order to maximize revenue.To find the maximum revenue, we will substitute [tex]x=150[/tex] in our given formula. [tex]y=-3(150)^2+900(150)-5,000[/tex][tex]y=-3*22,500+135,000-5,000[/tex][tex]y=-67,500+135,000-5,000[/tex][tex]y=62,500[/tex]Therefore, the maximum revenue would be $62,500.