SOLUTION: Rite-Cut riding lawnmowers obey the demand equation p= -1/20x+1,030. The cost of producing x lawnmowers is given by the function C(x)= 150x+3,000. a. Express the revenue R as a f

Question 918910: Rite-Cut riding lawnmowers obey the demand equation p= -1/20x+1,030. The cost of producing x lawnmowers is given by the function C(x)= 150x+3,000.
a. Express the revenue R as a function of x. Do not factor answer
b. Express the profit P as a function of x. Do not factor answer
c. Find the value of x that maximizes profit. What is the maximum profit?
d. What price should be charged in order to maximize profit?
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
p= -1/20x+1,030, C(x)= 150x+3,000.
a) R(x) = (-1/20)x + 1,030)x
...
b) P(x) = (-1/20)x + 1,030)x -( 150x+3,000)
P(x) = (-1/20)x^2 + 1,030x -150x-3,000)
P(x) = (-1/20)x^2 + 880x - 3000
...
c) x = -(880/(-1/10) = 8800, maximizes profit
...
d) p(8800) = (-1/20)8800 + 1030 = $590

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