Question

1. Annual demand for educational toys in the city of Lambert is 1,200 units. The fixed ordering cost is $41, and the holding cost is known to be always $2 per unit per year regardless of unit price. The contract offered by the supplier is an all-units discount and consists of the following price schedule:

Quantity	Unit Price
1 to 199	$ 27
200 to 299	$ 26
300 to 399	$ 25
400 or more	$ 24

1. What are the realizable EOQ(s)?

Answer:

2. If the largest realizable EOQ quantity in i) is ordered, what is the corresponding unit price applied by the supplier?

Answer:

3. Compare the total cost for the largest realizable EOQ in part i) with the total costs for all larger break points. What is the optimal order quantity?

Answer:

Answer 1

DEMAND = 1200

ORDERING COST = 41

HOLDING COST = 2

EOQ = SQRT(2 * DEMAND * ORDERING COST / HOLDING COST) = SQRT(2 * 1200 * 41 / 2) = 222

ANNUAL HOLDING COST = ADJUSTED EOQ / 2 * HOLDING COST PER UNIT

ANNUAL ORDERING COST = (ANNUAL DEMAND / ADJUSTED EOQ) * ORDERING COST

ANNUAL MATERIAL COST = ANNUAL DEMAND * OFFERED PRICE PER UNIT

TOTAL COST OF INVENTORY = ANNUAL(HOLDING + ORDERING + MATERIAL)

OPTIMAL ORDER QUANTITY = 400

ASSOCIATED COST = 29323

NO.	LOWER LIMIT	UPPER LIMIT	PER UNIT PRICE	HOLDING COST	EOQ	ADJUSTED QUANTITY	ANNUAL HOLDING COST	ANNUAL ORDER COST	ANNUAL MATERIAL COST	TOTCAL COST OF INVENTORY
1	0	199	27	2	222	199	199 / 2 = 199	1200 / 199 * 41 = 247.24	1200 * 27 = 32400	199 + 247.24 + 32400 = 32846
2	200	299	26	2	222	222	222 / 2 = 222	1200 / 222 * 41 = 221.62	1200 * 26 = 31200	222 + 221.62 + 31200 = 31644
3	300	399	25	2	222	300	300 / 2 = 300	1200 / 300 * 41 = 164	1200 * 25 = 30000	300 + 164 + 30000 = 30464
4	400	OR MORE	24	2	222	400	400 / 2 = 400	1200 / 400 * 41 = 123	1200 * 24 = 28800	400 + 123 + 28800 = 29323