Question

Suppose you plan to buy many blank compact disks. You check price lists and find out that

if you buy 100 CDs or fewer you pay $0.74 each. However, if you buy over 100 CDs the pricedrops to $0.69 for each additional CD up to 300.
(a)Write a function that describes the cost C(n) of n number of CDs purchased.
(b)What is the cost of 53 CDs?
(c)What is the cost for 201 CDs?

Answer 1

a) C(n) = 0.74 * min(n, 100) + 0.69 * max(n - 100, 0)
b) 39.22
c) 143.69

Explanation:

(a) We can write a piecewise function to describe the cost C(n) of n CDs purchased:

C(n) = 0.74 * min(n, 100) + 0.69 * max(n - 100, 0)

(b) The cost of 53 CDs is:

C(53) = 0.74 * min(53, 100) + 0.69 * max(53 - 100, 0) = 0.74 * 53 = 39.22

(c) The cost for 201 CDs is:

C(201) = 0.74 * min(201, 100) + 0.69 * max(201 - 100, 0) = 0.74 * 100 + 0.69 * 101 = 74 + 69.69 = 143.69