Question

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? ...?

Answer 1

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