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