Rite cut riding lawnmower obeys the demand equation p=-1/20x+1060. the cost of producing x lawnmowers is given by the function c(x)=120x+5000

a)express the revenue r as a function of x
b)express the profit p as a function of x
c)fine the value of x that maximizes profit. what is the maximum profit?
d)what price should be charged to maximize profit?

A.) Revenue = price * quantity = px = -1/20x^2 + 1060x
R(x) = -1/20x^2 + 1060x.

b.) Profit = Revenue - Cost = R(x) - C(x) = -1/20x^2 + 1060x - 120x - 5000
P(x) = -1/20x^2 + 940x - 5000

c.) For maximum profit, dP/dx = 0
-1/10x + 940 = 0
1/10x = 940
x = 940 * 10 = 9,400
x = 9,400
Maximum profit = P(9400) = -1/20(9400)^2 + 940(9400) - 5000 = $4,413,000

d.) The price to be charged for maximum profit = -1/20(9400) + 1060 = $590

Add up all the sides