Question

A mail-order house uses 16,260 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

a.	Determine the optimal order quantity. (Round your answer to the nearest whole number.)

Optimal order quantity

boxes

b.	Determine the number of orders per year. (Round your answer to 2 decimal places.)

Number of order

per year

Answer 1

DEMAND = 16260

HOLDING COST = 0.6

ORDERING COST = 96

EOQ = SQRT(2DS/H)

Optimal order quantity = Quantity with lowest total annual cost of inventory

TCI = annual holding cost + annual ordering cost + annual material cost

Annual holding = adjusted quantity / 2 * holding cost

Annual ordering = demand / adjusted quantity * ordering cost

Annual material cost = demand * cost per unit

ADJUSTED Q = EOQ IF EOQ > LOWER LIMIT, < UPPER LIMIT

LOWER LIMIT IF EOQ < LOWER LIMIT

UPPER LIMIT IF EOQ > UPPER LIMIT

NO.	LOWER BRACKET	UPPER BRACKET	PER UNIT	HC	EOQ	Q*	TOTAL COST	FORMULA
1	1	1999	1.25	0.6	2281	1999	21705.57	(16260 * 1.25) + ((1999 / 2) * 0.6) + ((16260 / 1999) * 96) = 21706
2	2000	4999	1.2	0.6	2281	2281	20880.63143	(16260 * 1.2) + ((2281 / 2) * 0.6) + ((16260 / 2281) * 96) = 20881
3	5000	9999	1.15	0.6	2281	5000	20511.19	(16260 * 1.15) + ((5000 / 2) * 0.6) + ((16260 / 5000) * 96) = 20511
4	10000	MORE	1.1	0.6	2281	10000	21042.1	(16260 * 1.1) + ((10000 / 2) * 0.6) + ((16260 / 10000) * 96) = 21042

OPTIMAL ORDER QUANTITY = 5000

TOTAL COST OF INVENTORY = 20511

2. NO. OF ORDERS PER YEAR = D / Q = 16260 / 5000 = 3.25

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