Respuesta :
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.
