Problem 7-30 Bryson Carpet Mills produces a variety of different carpets. Changi
ID: 339823 • Letter: P
Question
Problem 7-30 Bryson Carpet Mills produces a variety of different carpets. Changing from production of one carpet to another involves a setup cost of S3,100. Annual demand for this style is 183,000 yards. Bryson Carpet Mills produces carpet 300 days per year. The production process is most efficient when 8,100 yards per day are produced at a cost of $5.50 per yard. Inventory carrying cost is estimated at 15 percent annually What should be the production order quantity? (Round up your answer to the next whole number.) Production order quantityyardsExplanation / Answer
We will use here Production order Quantity[POQ] model to determine the optimum production order Quantity
POQ is given by following formula
POQ = Q = Sqrt [ 2DS/(H(1-d/p))]
Where D = Annual Demand
S = Setup Cost
H = Holding Cost per unit per year
d= demand rate
p= production rate
In this problem
D = 183,000 yards
S= $3100
In the given case Cost per yard = $ 5.5
Inventory Carrying cost = 15%
Hence H = (15/100)*5.5 = $ 0.825
Since here we know the annual demand and production rate we will consider the annual rates. It is important to use the same units i.e we should consider the demand and production rate both for the same period of time which in this case is 1 year
Units produced per day = 8100 [Most efficient production rate per day ]
Number of production days = 300
Annual production rate = 8100 * 300 =2,430,000
d/p = 183,000/2,430,000 = 0.0753
Thus Q = Sqrt [ (2 * 183000*3100) / (.0825* (1-.0753))]
=38565.24
When rounded off to next whole number the production lot comes out to be 38566 yards