SOLUTION: Find the number of units that produces a maximum revenue for R = 800x - 0.01x^2 where R is the total revenue (in dollars) for a cosmetics company and x is the number of unit

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Find the number of units that produces a maximum revenue for R = 800x - 0.01x^2 where R is the total revenue (in dollars) for a cosmetics company and x is the number of unit      Log On


   

Question 4788: Find the number of units that produces a maximum revenue for
R = 800x - 0.01x^2
where R is the total revenue (in dollars) for a cosmetics company and x is the number of units produced.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
This equation represents a parabola that opens downward, so the vertex of the parabola will be the point at which maximum revenue occurs. As in the last question that I posted, the vertex occurs at x = %28-b%29+%2F%282a%29, where a = coefficient of x%5E2 and b = coefficient of x. In this case a= -0.01 and b= 800.

Maximum revenue occurs at x=%28-b%29%2F%282a%29+=+%28-800%29%2F%282%2A%28-0.01%29%29=+800%2F0.02+= 40,000 units.
To find the maximum revenue, substitute x= 40,000 into the original equation for R and it turns out that R+=+800%2A40000+-+0.01%2A40000%5E2 or $16,000,000.

R^2 at SCC