Question

A digital media company is ordering booklets to promote their business. The manufacturer charges $0.50 for each booklet when 50 or fewer are ordered,$0.45 for each booklet when 51 to 100 booklets are ordered,

0.40foreachbookletwhen101to250bookletsareordered,and 0.35 for each booklet when 251 or more booklets are ordered. Each order consists of a $10 shipping charge, no matter the size of the order. a) Write a piecewise-defined function describing the cost of ordering booklets. b) What is the cost of purchasing 132 booklets? What it is the cost of purchasing 518 booklets?

Answer 1

a) The piecewise-defined function describing the cost of ordering booklets depends on the number of booklets ordered. b) The cost of purchasing 132 booklets is $52.80, and the cost of purchasing 518 booklets is $181.30.

Step-by-step explanation:

a) To write a piecewise-defined function describing the cost of ordering booklets, we need to consider the different price tiers based on the number of booklets ordered. Let's break it down:

- If 50 or fewer booklets are ordered, the cost per booklet is $0.50. Therefore, for x ≤ 50, the cost function is C(x) = 0.50x.

- If 51 to 100 booklets are ordered, the cost per booklet is $0.45. Therefore, for 51 ≤ x ≤ 100, the cost function is C(x) = 0.45x.

- If 101 to 250 booklets are ordered, the cost per booklet is $0.40. Therefore, for 101 ≤ x ≤ 250, the cost function is C(x) = 0.40x.

- If 251 or more booklets are ordered, the cost per booklet is $0.35. Therefore, for x ≥ 251, the cost function is C(x) = 0.35x.

b) The cost of purchasing 132 booklets falls within the range of 101 to 250 booklets, so we will use the cost function C(x) = 0.40x. Plugging in x = 132, we have C(132) = 0.40 * 132 = $52.80. The cost of purchasing 518 booklets falls within the range of 251 or more booklets, so we will use the cost function C(x) = 0.35x. Plugging in x = 518, we have C(518) = 0.35 * 518 = $181.30.