2. (20 pt) Montegut Manufacturing produces a product for which the annual demand

Question

2. (20 pt) Montegut Manufacturing produces a product for which the annual demand is 10,000 units. Production averages 100 units per day, while demand is 40 units per day. Holding costs are $2.00 per unit per year, and setup cost is $200.00. a) If the firm wishes to produce this product in economic batches, what size batch should be used? (Keep answer integer.) b) What is the maximum inventory level? (Keep answer integer.) c) How many order cycles are there per year? d) What are the total annual holding and setup costs? pok max

Explanation / Answer

Annual demand (D) = 10000 units

Setup cost (S) = $200

Holding cost (H) = $2

Production rate (p) = 100 units per day

Demand rate (d) = 40 units per day

a) Economic production quantity(Q)= sqrt of{2DS/H [1-(d/p)]}

= sqrt of {(2 x 10000 x 200)/2[1-(40/100)]}

= sqrt of (4000000/1.20)

= sqrt of 3333333.33

= 1825.7 or rounded to 1826 units

b) Maximum inventory(Imax) = (Q/p)(p-d) = (1826/100)(100-40)= 18.26 x 60 = 1095.6 or rounded to 1096 units

C) Order cycle per year = (D/Q) = 10000/1826 = 5.48

d) Annual holding cost = (Imax/2)H = (1096/2)2 = $1096

Annual setup cost = (D/Q) S = (10000/1826)200 = $1095.29

Total annual cost = Holding cost + setup cost = $1096 + $1095.29 = $2191.29

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