1. Walmart makes fresh pumpkin pies each morning. The daily demand for these pie
ID: 458826 • Letter: 1
Question
1. Walmart makes fresh pumpkin pies each morning. The daily demand for these pies is a random variable with a distribution estimated from manager Mike’s experience given by
Number of pumpkin Probability
pies sold in one day
0 0.05
5 0.15
10 0.10
15 0.05
20 0.20
25 0.10
30 0.15
35 0.05
40 0.10
45 0.05
Mike knows that the cost of making one pumpkin pie is about $4. In the store, pumpkin pies are sold for $10 each. At the end of the day, unsold pumpkin pies are sold to Bowling Green food bank for $1 each. Determine the average number of pumpkin pies sold to Bowling Green food bank (Average Overstock).
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2. Daily demand for the ice creams at I-Scream parlor is normally distributed with a mean of 100 quarts and a standard deviation of 30 quarts. The owner has the ice cream supplied by a wholesaler who charges $3 per quart. The wholesaler charges a $80 delivery charge regardless of order size. The opportunity cost of capital to I-Scream is estimated to be 20% per year. Assume 365 days in the year. What is the optimal order size of each order?
3.Walmart makes fresh pumpkin pies each morning. The daily demand for these pies is a random variable with a distribution estimated from manager Mike’s experience given by
Number of pumpkin Probability
pies sold in one day
0 0.05
5 0.15
10 0.10
15 0.05
20 0.20
25 0.10
30 0.15
35 0.05
40 0.10
45 0.05
Mike knows that the cost of making one pumpkin pie is about $4. In the store, pumpkin pies are sold for $10 each. At the end of the day, unsold pumpkin pies are sold to Bowling Green food bank for $1 each. How many pumpkin pies should Kroger make at the start of each day?
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4.Walmart makes fresh pumpkin pies each morning. The daily demand for these pies is a random variable with a distribution estimated from manager Mike’s experience given by
Number of pumpkin Probability
pies sold in one day
0 0.05
5 0.15
10 0.10
15 0.05
20 0.20
25 0.10
30 0.15
35 0.05
40 0.10
45 0.05
Mike knows that the cost of making one pumpkin pie is about $4. In the store, pumpkin pies are sold for $10 each. At the end of the day, unsold pumpkin pies are sold to Bowling Green food bank for $1 each. Determine the average number of customers turned away (Average Understock).
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show me the work please.
Thanks.
Explanation / Answer
1) The average Number of Pumkins Sold to
For Finding Average overstock we have to apply newsvendor Model C2/(C1+C2), where C1 is the cost of the items and C2 is the cost of Unsold
C1= $4, C2= if Unsold , there is a loss in profit of $6 but resale value of $1 = $6-$1= $5
News vendor Model = 5/(4+5) = 0.555 . This is the value of Z.
In order to find the number of units is Overstocked we have to get X , The value of X is getting from Z= (X-Mean)/SD.
So we have to calculate Mean and Standard Deviation
Mean = E(X) = 0*0.05+5*0.15+10*0.10+................+45*0.05= 21.5
Variance = E(x2 )-E(X)2 =
E(x2 )= 02*0.05+52*0.15+102 *0.10+...............+452*0.05 = 625
V(x)= E(x2 )-E(X)2 = 625-21.52= 162.75
SD= Square root V(x) = square root (162.75) = 12.75
Z= (X-Mean)/SD
Z= (X-21.5)/12.75
The probability of =0.5555 is at when Z= 0.14
So
0.14 = (X-21.5)/12.75
X= 0.14*12.75+21.5=23.285
Anything Above 23 units is Overstock.
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