An office copier has an initial price of
$2,500. A service contract costs $200 for the first year and
increases $50 per year thereafter. It can be shown that the
total cost of the copier after n years is given by
C1n2 = 2,500 + 175n + 25n2
The average cost per year for n years is given by
C1n2 = C1n2 >n.
(A) Find the rational function C.
(B) Sketch a graph of C for 2 < n <20.
(C) When is the average cost per year at a minimum, and
what is the minimum average annual cost? [Hint: Refer
to the sketch in part (B) and evaluate C1n2 at appropriate
integer values until a minimum value is found.] The time
when the average cost is minimum is frequently referred
to as the replacement time for the piece of equipment.