Healthy Plants Ltd. (HP) produces its premium plant food in 50-pound bags. Deman
ID: 428794 • Letter: H
Question
Healthy Plants Ltd. (HP) produces its premium plant food in 50-pound bags. Demand for the product is 10,000 pounds per week. HP operates fifty weeks per year and can produce 22,000 pounds per week. The setup cost is $200 and the annual holding cost rate is $0.39 per bag. Currently, HP produces its premium plant food in batches of 1,200,000 pounds.
Calculate the maximum inventory level for HP according to its current operating policy.
Calculate the total annual costs of this operating policy.
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Healthy Plants Ltd. (HP) produces its premium plant food in 50-pound bags. Demand for the product is 10,000 pounds per week. HP operates fifty weeks per year and can produce 22,000 pounds per week. The setup cost is $200 and the annual holding cost rate is $0.39 per bag. Currently, HP produces its premium plant food in batches of 1,200,000 pounds.
Explanation / Answer
Annual demand of plant food for HP = D = 10,000 / week x 50 weeks = 500,000 pounds
Weekly demand for plant food = d = 10,000 pounds
Weekly production per week = p = 22,000 pounds
Set up cost = Cs = $200
Weight of 1 bag = 50 pounds
And annual holding cost rate per bag = $0.39
Therefore , annual holding cost rate per pound = $0.39 /50 = $0.0078 per pound
Maximum inventory level for HP as per current policy
= Current order quantity x ( 1 – d/p)
= 1,200,000 x ( 1 – 10,000/22,000)
= 1,200,000 x 0.5454
= 654,480 pound
Number of batches in a year
= annual demand/ batch production quantity
= 500,000/1,200,000
= 5/12
Annual set up cost
= Set up cost x number of set ups
= $200 x 5/12
= $83.33
Annual holding cost
= Holding cost per pound x average inventory ( pounds)
= $0.0078 x Maximum inventory / 2
= $0.0078 x 654480/2
= $2552.47
Total annual cost of this operating policy
= Annual set up cost + annual holding cost
= $83.33 + $2552.47
= $2635.80
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