Problema Solution
The John Deere company has found that the revenue, in dollars, from sales of riding mowers is a function of the unit price, p, in dollars that it charges. If the revenue is R(p)= -1/2p^2 +1900p. What unit price p should be charged to maximize revenue? What is the maximum revenue ?
Answer provided by our tutors
We need to find the maximum for the parabolic function:
R(p)= -1/2p^2 +1900p.
R max = c - b^2/4a
a = -1/2
b = 1900
c = 0
R max = 0 - 1900^2/(4*(-1/2))
R max = $1,805,000
The maximum revenue is 1,805,000.
p max = -b/2a
p max = -1900/(2*(-1/2))
p max = $1,900
To maximize revenue the unit price should be changed to $1,900.