A company manufacturers and sells x televisions per month. The monthly cost and and revenue equations are:

c(x) = 82,000 +50x, for 0

Question

A company manufacturers and sells x televisions per month. The monthly cost and and revenue equations are: 

c(x) = 82,000 +50x, for 0<x<9000 (they're actually less than/equal to signs)

R(x)= 500x - 1/30x^2

I need to find the minimum cost, max revenue, and maximum profit, but I'm stuck on max revenue and maximum profit. Could someone please explain how to get the max. revenue and how to use that to get the max profit?

anonymous · Answer

R(x)= - (1/30) x² + 500x
  R'(x) = - (1/15) x  + 500
  R'(x) = 0  -->   x = 500 * 15 = 7,500 televisions

anonymous · Answer

-> Max Revenue:
     R ( 7, 500 ) = ....

anonymous · Answer

Would I plug in 7500 back to the original equation of 82,000 +50x, or is that something different?

anonymous · Answer

R ( x  )       = - (1/30) x² + 500x 
R ( 7, 500 ) =  - (1/30) 7, 500 ² + 500 *7, 500