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Question 920574: Rite-Cut riding lawnmowers obey the demand equation p= -1/20x+1070. The cost of producing x lawnmowers is given by the function C(x)= 110x+6,000.
a. Express the revenue R as a function of x. Simplify answer, do not factor.
b. Express the profit P as a function of x. Simplify answer, do not factor
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+1070, C(x)= 110x+6,000
a) R = px = (-1/20)x^2 + 1070x
.......
b) P = (-1/20)x^2 + 1070x - 110x - 6000
P = (-1/20)x^2 + 960x - 6000
......
c) P = (-.05)(x - 9600)^2 + $4,602,000
x = 9600 maximizes profit to $4,602,000
.......
d) p= -1/20(9600)+1070 = $590
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