The CarryItAll mini-van, a popular vehicle among soccer moms, obeys the demand e
ID: 3186259 • Letter: T
Question
The CarryItAll mini-van, a popular vehicle among soccer moms, obeys the demand equation
ppequals=negative StartFraction 1 Over 50 EndFraction x plus 13 comma 000?150x+13,000.
The cost of producing
xx
vans is given by the function Upper C left parenthesis x right parenthesis equals 9960 x plus 20 comma 000.C(x)=9960x+20,000.
a) Express the revenue
Upper RR
as a function of
xx.
b) Express the profit
Upper PP
as a function of
xx.
c) Find the value of
xx
that maximizes profit. What is the maximum profit?
d) What price should be charged in order to maximize profit?
Explanation / Answer
a) revenue R(x) = x ( -1/50 x + 13000 )
R(x) = - x^2/50 + 13000 x
b) profit = revenue - cost
= - x^2/50 + 13000 x - 9960x - 20000
P(x) = - x^2/20 + 3040 x - 20000
c) value of x that maximizes profit = - 3040 / 2 ( -1/20)
x = 30,400
maximum profit = - (30400)^2/20 + 3040 (30400) - 20000
= $ 46188000
d) price in order to maximize profit
= -1/50 ( 30400) + 13000
= $ 12392