M7_A2. Dillsboro Publishing Company produces books for the retail market. Demand for a current book on quantitative analysis is expected to be a constant 8900 copies per year. The cost of one copy is a very reasonable $29.99 per copy. The holding cost is 16% annual rate and production setup costs are $200 per setup. The equipment on which the book is produced has an annual production volume of 25,000 copies. Dillsboro has 250 working days per year. a) What is the optimal production lot size? b) What is the average number of production runs per year? c) What is the maximum inventory that will be held? d) What is the total annual holding cost? e) What is the total annual setup cost? f) What is the length of a production run (in days)?
We have to use the formula derived from the Economic Order Quantity model.
q* --> Optimal order quanity
Q --> Annual demand = 8900
s --> Set-up cost = 200
h --> holding cost = 0.16*29.99 = 4.8
n --> Number of productions per year
c) Maximum inventory = 861
It happens immedietly after a production run.
d) Average inventory = 861/2 = 430.5
Therefore, annual holding cost = 430.5 * 4.8= $ 2066.4
e) Annual set up cost = 10.3*200 = $2060
f) Average production per day = 25000/250 =100
Length of production run = 861/100 = 8.6 or approximately 9 days
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