2. DVD Player Company
A DVD player company's weekly production costs, denoted by C , is given by the
where x is the selling price of DVD players produced, in pounds. The number of
DVD players sold each week is given by S= 400 -x and the weekly revenue is
given by R = Sx . The weekly profit, P , can be found by subtracting weekly costs
from the weekly revenue.
(a) Find an expression for R in terms of x only and hence show that
P= -5x2 + 390x- 30 .
(b) Find the value of x at which P takes its maximum value. What is the maximum
(c) Copy and complete the following table.
X 0 10 25 35 45 55 80
Maximum profit is found using derivatives. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.