Derivatives and Maximum Profit
DVD Player Company
A DVD player company’s weekly production costs, denoted by C, is given by the expression:
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= -5×2 + 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
On graph paper plot the function P.
(d) By solving an equation, find the values of x for which P is at least £4500.