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Production model for inventory management

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Frank's machine shop operates 250 days per year. Frank sells 5,000 units per year of his most popular item, a specialty gear. The setup cost for this gear is $100 and the monthly unit cost of holding inventory is 1% of the production cost per unit, which is $50. The lead time is 10 days. When the gear is being produced, the shop can make 80 gears per day (Hint: You should use the production model for inventory management).

1) How many gears should be produced in each run at what minimum cost?
2) What is the cycle time?
3) Find the reorder point.
4) Draw a graph to depict inventory level against time and show on it the quantities found above. Also, what is the maximum inventory level.

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The production model for inventory management: Frank's machine shop

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