Question

A mail-order house uses 17,650 boxes a year. Carrying costs are 60 cents per box a year, and ordering costs are $96. The following price schedule applies.

Number of Boxes	Price per Box
1,000 to 1,999	$1.25
2,000 to 4,999	1.20
5,000 to 9,999	1.15
10,000 or more	1.10

Answer 1

DEMAND = 17650

ORDERING COST = 96

HOLDING COST = 0.6

THEORY

EOQ = SQRT(2 * DEMAND * ORDERING COST / HOLDING COST)

Q* = ADJUSTED QUANTITIY BETWEEN THE UPPER AND LOWER LIMIT AND THE EOQ

AHC = ANNUAL HOLDING COST = (Q* / 2) * HOLDING COST PER UNIT

AOC = ANNUAL ORDERING COST = (DEMAND / Q*) * ORDERING COST

APC = ANNUAL PURCHASING COST = DEMAND * Q*

TCI = TOTAL COST OF INVENTORY = AHC + AOC + APC

NO.	LOWER LIMIT	UPPER LIMIT	PER UNIT	HOLDING COST	EOQ	Q*	AHC	AOC	APC	TCI
1	0	1999	1.25	0.6	2377	1999	(1999 / 2) * 0.6 = 599.7	(17650 / 1999) * 96 = 847.62	17650 * 1.25 = 22062.5	599.7 + 847.62 + 22062.5 = 23509.82
2	2000	4999	1.2	0.6	2377	2377	(2377 / 2) * 0.6 = 713.1	(17650 / 2377) * 96 = 712.83	17650 * 1.2 = 21180	713.1 + 712.83 + 21180 = 22605.93
3	5000	9999	1.15	0.6	2377	5000	(5000 / 2) * 0.6 = 1500	(17650 / 5000) * 96 = 338.88	17650 * 1.15 = 20297.5	1500 + 338.88 + 20297.5 = 22136.38
4	10000	& more	1.1	0.6	2377	10000	(10000 / 2) * 0.6 = 3000	(17650 / 10000) * 96 = 169.44	17650 * 1.1 = 19415	3000 + 169.44 + 19415 = 22584.44

OPTIMAL ORDER QUANTITY = 5000

TOTAL COST OF INVENTORY = 22136