Question

In: Operations Management

9. The price of an item depends on the order quantity: (ignore this row) Less than...

9. The price of an item depends on the order quantity:

(ignore this row)
Less than 100 pounds	$	20	per pound
100 pounds to 999 pounds	$	19	per pound
1,000 pounds or more	$	18	per pound

It costs $40 to place each order. Annual demand is 3,000 units. Carrying cost is 25 percent of the material price.

What is the optimal order quantity, and what would be its annual total cost? Go to at least two decimal places for your intermediate calculations. Round your answers to the nearest whole number.

Optimal order quantity		pounds
Total annual cost		(ignore this cell)

Expert Solution

OPTIMAL ORDER QUANTITY = 1000

TOTAL COST FOR OPTIMAL QUANTITY = 56370

DEMAND = 3000

ORDERING COST = 40

HOLDING COST % = 25 %

EOQ = SQRT(2 * D * S / H), WHERE D = DEMAND, S = ORDERING COST, H = HOLDING COST

ANNUAL HOLDING COST = (Q* / 2) * H

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

ANNUAL PURCHASE COST = DEMAND * PER UNIT COST IN PARTICULAR PRICE BRACKET

TCI = AHC + AOC + APC

OPTIMAL ORDER QUANTITY = 1000

TOTAL COST FOR OPTIMAL QUANTITY = 56370

#	MINIMUM QUANTITY	MAXIMUM QUANTITY	UNIT COST	ADJUSTED HOLDING COST	Q	Q*	AHC	AOC	APC	TCI
1	0	99	20	5	219	99	(99 / 2) * 5 = 247.5	3000 / 99 * 40 = 1212.12	3000 * 20 = 60000	247.5 + 1212.12 + 60000 = 61460
2	100	999	19	4.75	225	225	(225 / 2) * 4.75 = 534.38	3000 / 225 * 40 = 533.33	3000 * 19 = 57000	534.38 + 533.33 + 57000 = 58068
3	1000	OR MORE	18	4.5	231	1000	(1000 / 2) * 4.5 = 2250	3000 / 1000 * 40 = 120	3000 * 18 = 54000	2250 + 120 + 54000 = 56370

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keosha answered 1 month ago

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