quantitative decisions in business This assignment must be in Excel/QM and submi
ID: 411572 • Letter: Q
Question
quantitative decisions in business
This assignment must be in Excel/QM and submitted through Assignment. Also provide a written response for each part of each question.
3.3) Orders for clothing from a particular manufacturer for this year's Christmas shopping season must be placed in February. The cost per unit for a particular dress is $20 while the anticipated selling price is $50. Demand is projected to be 50, 60, or 70 units. There is a 40 percent chance that demand will be 50 units, a 50 percent chance that demand will be 60 units, and a 10 percent chance that demand will be 70 units. The company believes that any leftover goods will have to be scrapped. How many units should be ordered in February?
Explanation / Answer
Given are the following data :
Cost per dress = C = $20
Price per dress = P = $50
Salvage value = S = 0 ( since leftover goods need to be scrapped )
Thus,
Underage cost = Cu = P – C = $50 - $20 = $30
Overage cost = Co = C – S = $20 – 0 = $20
Thus , Critical Ratio = Cu/ ( Cu + Co ) = 30 / ( 30 + 20 ) = 30/50 = 0.60
Critical ratio corresponds to the probability of demand for optimum quantity which should be ordered.
Therefore , probability that demand will be at least the optimum quantity will be 0.60
Following table presents probability values corresponding to cases that demand will be minimum of the respective values :
Demand will be at least below quantity
Corresponding probability
40
1
60
0.60
70
0.10
Note:
Corresponding probability is calculated as : 1 - Cumulative percentages of all preceeding quantities/ 100
Therefore optimum quantity which should be ordered in February = 60 units
60 UNITS SHOULD BE ORDERED IN FEBRUARY
Given are the following data :
Cost per dress = C = $20
Price per dress = P = $50
Salvage value = S = 0 ( since leftover goods need to be scrapped )
Thus,
Underage cost = Cu = P – C = $50 - $20 = $30
Overage cost = Co = C – S = $20 – 0 = $20
Thus , Critical Ratio = Cu/ ( Cu + Co ) = 30 / ( 30 + 20 ) = 30/50 = 0.60
Critical ratio corresponds to the probability of demand for optimum quantity which should be ordered.
Therefore , probability that demand will be at least the optimum quantity will be 0.60
Following table presents probability values corresponding to cases that demand will be minimum of the respective values :
Demand will be at least below quantity
Corresponding probability
40
1
60
0.60
70
0.10
Note:
Corresponding probability is calculated as : 1 - Cumulative percentages of all preceeding quantities/ 100
Therefore optimum quantity which should be ordered in February = 60 units
60 UNITS SHOULD BE ORDERED IN FEBRUARY
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