# Solved: The Dine Corporation is both a producer and a user of brass couplings. The firm operates 200 days a

The Dine Corporation is both a producer and a user of brass couplings. The firm operates 200 days a year and uses the couplings at a steady rate of 75 per day. Couplings can be produced at a rate of 100 per day. Annual storage cost is \$1.5 per coupling, and machine setup cost is \$50 per run.
(1)Determine the economic run quality
(2)How many runs per year will there be?
(3)Compute the maximum inventory level
(4)Determine the length of the pure consumption portion of the cycle

= rate of demand = 75 per day

D = annual demand = 75*200 = 15000

p = prodution rate = 100 per day

IC = carrying cost per item per year = \$1.5

S = setup cost per setup = \$50

The formula for Economic run quantity is

So, Qp* = sqrt(2*15000*50*100 / (1.5*(100-75))) = 2000 —————————(1)

No. of Runs = D / Qp* = 15000/2000 = 7.5 or after rounding of 8 runs —————–(2)

Maximum inventory = (1 – d/p) * Qp* = Qp* / 4 = 500 ——————–(3)

Length of the cycle = Qp* / d = 2000/75 = 26.667 days

Length of run = Qp* / p = 2000/100 = 20 days

Length of the pure consumption portion of the cycle = Length of the cycle – Length of run =6.667 days ———-(4)

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