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1. Derive a formula for the following quantities for a production order quantity (POQ) model (a.k.a...

1. Derive a formula for the following quantities for a production order quantity (POQ) model (a.k.a EPQ model) with planned shortages.

(a) Size of optimal production quantity

(b) Maximum on-hand inventory level

(c) Average on-hand inventory level

(d) Optimal length of each cycle

(e) Fraction of a cycle we produce
(f) Fraction of a cycle we do not produce

(g) Optimal amount of backorder (quantity of backlogged items) (h) Optimal total cost

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