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A steel rolling mill can produce I-beams at the rate of 20 tons per week. Customer demand for the beams is 5 tons per week. To produce I-beams, the mill must go through a setup that requires changing to the appropriate rolling patterns. Each setup costs the mill $10,000 in labor and lost production. I-beams cost the mill $2,000 per ton and the mill has an annual holding cost of 25 percent. What is the optimal production batch size for I-beams?

Respuesta :

TomShelby

Answer:

the optimal production to reduce the inventory cost will be of 102 units per batch

Explanation:

We solve using the EOQ Economic Order Quantity:

[tex]Q_{opt} = \sqrt{\frac{2DS}{H}}[/tex]

Where:

D = annual demand = 260 (5 ton per week x 52 week per year)

S= setup cost = ordering cost = 10,000

H= Holding Cost = (2,000 x 25% holding cost) = 500.00

[tex]Q_{opt} = \sqrt{\frac{2(260)(10,000)}{500}}[/tex]

EOQ = 101.9803903 = 102

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