Valentine\'s Day is coming soon and your supervisor at the local HallwayMark Car
ID: 380377 • Letter: V
Question
Valentine's Day is coming soon and your supervisor at the local HallwayMark Cards is concerned about ordering cases of cards. She does not want to stock too many or too few. But she has captured detailed information over time on sales. HallwayMark Cards purchases cases of cards for $45 and sells them for $115. If HallwayMark Cards is not able to sell all cases of cards during the Valentine's Day season, then the cases can be returned to the supplier for a salvage credit of $10 dollars per case. Your supervisor thinks that HallwayMark Cards can improve profits by ordering just the right amount and asks you to help her determine how many cases of cards HallwayMark Cards should order this year. You know that HallwayMark Cards orders in quantity multiples of 15, and you have calculated the independent probabilities of sales and created the following table.
Sales of cases of cards
50
65
80
95
110
125
140
155
170
185
Probability
0.05
0.06
0.09
0.21
0.34
0.12
0.07
0.03
0.02
0.01
Complete the following table:
Important! Round cost of stocking out and overstocking to nearest whole number and enter as ## (e.g. “2” or “14”) Round in-stock probability naturally to 2 digits and enter as 0.00. For example, if your calculated answer is 0.784 you would enter 0.78. Round the order quantity up and enter as ###.
Cost of stocking out (Cu)
$
Cost of overstocking (Co)
$
Optimal in-stock probability
(p* (= F(Q*))
How much should she order?
Please show me the formulas! I want to learn how to do them and not just get an answer. If you're using excel just show me the formulas so that I can follow them! I won't be able to use Excel on my Exam.Thank you very much!
Sales of cases of cards
50
65
80
95
110
125
140
155
170
185
Probability
0.05
0.06
0.09
0.21
0.34
0.12
0.07
0.03
0.02
0.01
Explanation / Answer
Given are following data :
Unit purchase cost of cards = C = $45
Unit sales price of cards = P = $115
Salvage price of card = S = $10
Hence,
Cost of stockout ( Cu) = P – C = $115 - $45 = $70/unit
Cost of overstocking ( Co) = C – S = $45 - $10 = $35/ unit
Thus Critical ratio or Optimum in stock probability
= Cu/ ( Cu + Co)
= 70 / ( 70 + 35)
= 70/105
=0.666 ( 0.67 rounded to nearest whole number )
IN STOCK PROBABILITY = 0.67
Following table illustrates probabilities of various minimum demand quantities :
Minimum demand quantity
With in stock probability of. 0.67 , quantity thus should be ordered will be 95 ( probability : 0.80) and 110 ( probability :0.59).
On a prorate basis, corresponding quantity for probability 0.67 will be
= 95 + ( 110 – 95) x ( 0.67 – 0.59) / ( 0.80 – 0.59)
= 95 + 15 x 0.08/0.21
= 95 + 5.71
= 100.71
Since quantity to be ordered will be in multiples of 15 , the nearest value to 100.71 which is multiple of 15 is 105
Thus, she should order 105 cards
COST OF STOCKING OUT ( Cu): $70
COST OF OVERSTOCKING ( Co): $35
OPTIMAL IN STOCK PROBABILITY : 0.67
HOW MUCH SHE SHOULD ORDER : 105 CARDS
Minimum demand quantity
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