Suppose that a plant manager has taken MgtOp 340, and so she uses economic batch sizes for production of a product. Suppose further that the setup cost is $50, the holding cost per unit per year is $10, the annual demand is 30,000 units, the firm operates (and experiences demand) 300 days per year, and the production rate per day is 1000 units. What will be the maximum inventory level that this product ever reaches?

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Business

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8 July, 16:23

Suppose that a plant manager has taken MgtOp 340, and so she uses economic batch sizes for production of a product. Suppose further that the setup cost is $50, the holding cost per unit per year is $10, the annual demand is 30,000 units, the firm operates (and experiences demand) 300 days per year, and the production rate per day is 1000 units. What will be the maximum inventory level that this product ever reaches?

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Carmelo Hogan · Answer 1

Maximum inventory level is 520 units

Explanation:

Given,

C0 = $50

Ce = $10

D = 30,000 units

d = D / Days

= 30,000 / 300

= 100 units per day

p = 1,000 units

Computing the optimal order size with the formula as:

Qopt = √ 2 C0 D / Ce (1 - d / p)

=√ 2 (50) (30,000) / $10 (1 - 100 / 1,000)

= 577.36

Computing the maximum inventory level as:

Maximum inventory level = Qopt (1 - d / p)

= 577.36 (1 - 100 / 1,000)

= 519.624 unit or 520 units