e. Slope of E Bryson Carpet Mills produces a variety of different carpets. Chang
ID: 362750 • Letter: E
Question
e. Slope of E
Bryson Carpet Mills produces a variety of different carpets. Changing from production of one carpet to another involves a setup cot of $1,000. One particular carpet costs $5 per yard to produce. Annual demand for this style is 120,000 yards. BCM produces carpet 300 days per year. The production process is most efficient when 4,000 yards per day are produced. Inventory carrying cost is estimated at 20% annually. Use this graph to answer questions 45 to 50 T1 T2 1.3 12. iWhat does the slope of line C represent? (Refer to the graph above) a. Maximum Inventory = 14,900 yards b. Rate of production per unit time 4,000 yards C. Rate of increase in inventory per unit time = 3,700 units d. Usage rate of accumulated inventory per unit time400 yards e. None of the aboveExplanation / Answer
Following data re to be noted:
‘d = Daily demand of carpet = 120,000 yards / 300 days = 400 yards / day
‘p = Daily production capacity = 4000 yards/ day
D = Annual demand = 300,000
Cs = Set up cost = $1000
Ch = Annual inventory carrying cost per yard = 20% of $5 = 1
Therefore , Economic production quantity ( EPQ ) to optimize cost
= Square root ( 2 x Cs x D / Ch x ( 1 – d/p) )
= Square root ( 2 x 1000 x 120,000/ 1 x ( 1 – 400/4000))
= Square root ( 2 x 1000 x 120,000/ 1 x 0.9)
= 16329.93 ( 16330 rounded to one decimal place )
Thus , Economic Production Quantity ( EPQ ) = 16329
Maximum inventory = EPQ x ( 1 – d/p) = 16329 x ( 1 – p /d) = 0.9 x 16330 = 14697
Production order frequency = EPQ/p = 16330/4000 = 4.082 days
Therefore, rate of increase in inventory per unit time 14697 / 4.082 = 3600 ( This is nearest to the value of 3700 units as quoted in 12.C)
Answer to question 12:
Answer : 12.C – Rate of increase in inventory per unit time = 3700
Answer to question 1 :
Slope of Line A is rate of production i.e. 4000 / day
Therefore , dashed line should represent maximum possible production in each production cycle
Therefore answer is “None of the above “
Answer to question 2:
Dashed line D represents maximum Inventory
( Remarks : The calculated value of maximum inventory is 14697which is nearest to value 14900 )
Answer to question 3 :
The period between T1 and T2 is when the production is when and the inventory is getting accumulated
Therefore , correct answer would be “ 3.e” i.e. option a and option c
Answer to question 4 :
Once peak inventory after every production run is reached , the peak inventory gets depleted at a steady rate upto zero.
The answer is “ b. Time at which accumulated inventory of the item is being used “
Answer to question 5:
Slope of C represents the rate at which inventory of the item is increasing in each production day
Answer to Question 2 :
Annual demand of engine = D = 46 engines / month x 12 month = 552
Ordering cost = Co = $2500
Annual unit holding cost = Ch = 5% of product cost = 5% of $65,000 = $3250
Thus,
Economic order Quantity ( EOQ )
= Square root ( 2 x Co x D / Ch )
= Square root ( 2 x 2500 x 552 / 3250)
= 29.14 ( 29 rounded to nearest whole number )
ECONOMIC ORDER QUANITY = 29
ECONOMIC ORDER QUANITY = 29
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