Question

A company uses the finite replenishment model to determine the optimal quantity to produce. There are days a year over which demand and production occur. The daily demand is ​, and the production rate is per day. The setup cost for production is ​$ per setup. Assuming that the carrying cost is percent of the​ item's ​$ ​cost, what is the​ length, in​ days, of a production run if the company produces the replenishment quantity that minimizes its​ inventory-related costs?

Answer 1

16.1 days

Step-by-step explanation:

Note: The full question is attached as picture below

Daily demand d = 520

Annual demand D = 520*250 = 130000

Setup cost S = $680

Production rate p = 875

Holding cost H = 0.25*25 = 6.25

Optimal order quantity Q

`Q = √(2DS/H)`
`√(p / p -d)`

`Q = √((2*130000*680)/6.25) √(875/875-520)`

Q = 8350

Length of production run = Q/d

Length of production run = 8350/520

Length of production run = 16.05769230769231

Length of production run = 16.1 days