A newsboy sells newspapers and his goal is to maximize profit. He kept a record
ID: 334736 • Letter: A
Question
A newsboy sells newspapers and his goal is to maximize profit. He kept a record of his sales for 125 days with the following result. His ordering policy is to order an amount each day that is equal to the previous day's demand. A newspaper costs the carrier 50 cents and he sells it for $1.00. Unsold papers are returned and he receives 25 cents (for a loss of 25 cents).
Newspapers demand per day
Number
of days
15
10
16
20
17
42
18
31
19
12
20
10
Total
125
Newspapers demanded
per day
Number of Days
Probability
Cumulative Probability
15
10
0.08
0.08
16
20
0.16
0.24
17
42
0.336
0.58
18
31
0.248
0.82
19
12
0.096
0.92
20
10
0.08
1
Total
125
1.864
3.64
Use the information and random numbers given in the table below to simulate the sale of newspapers for 10 days.
Day
Demand
Random Number
Quantity Ordered
Sales
Unsatisfied Demand
Unsold Papers
1
.78
18
2
.43
3
.93
4
.87
5
.48
6
.84
7
.87
8
.27
9
.20
10
.52
12. After completing the simulation, determine his total revenue for the ten days. _____
13. After completing the simulation, determine the monetary losses that result from unmet demand and unsold papers. _____
Newspapers demand per day
Number
of days
15
10
16
20
17
42
18
31
19
12
20
10
Total
125
Explanation / Answer
First of all, we will create a class table for random numbers using the cumulative probability give in the question. Need to take care of not repeatin the values while creating the class and stating it with 0 to end with 99. before moving ot the class, need to analyze the random numbers given. As the random numbers fall between 0 to 1, the class should be 0 to 0.99 which can include all the random numbers. The table will be as shown below.
Now the next step would be to assign the class to the random numbers and check the demand for that class. For example, 0.78 falls within the range of 0.58 to 0.81 which has the demand of 18 newspapers. By this way, we will find all the demands.
After that, we will calculate the order quantity. It is mentioned in the sum that the order quantity is the demand quantity if the previoue day. so the demand of the first day i.e., 18 will be the order quantity for the second day. By this way, we will find all the order quantities.
Now the sale would be the least of both, i.e., demand and order as we can not sale more than demand or the quantity we have ordered. By this way, we will get the sales for ten days which is of 173 newspapers is the answer to the first question.
The table below gives all the details we have calculated.
Now, to calculate the total revenue, we need to consider the total quantities of sales and unsold newspapers. the formula for the same wiil be as follows
Revenue = Sales Price + Scrape Price
Revenue = (173*1) + (7*0.25) = 174.75
We need to remember that revenue is asked and not the profit. so total income from sales should be consiered i.e., of selling all the 180 ordered quantities.
The monetary loss for unmet demand will be Selling Price of Unmet Demand - Cost Price of Unmet Demad = (6*1) - (6*0.5) = 3
The monetary loss for unsold newspapers will be Cost Price of Unsold newspapers - Selling Price of unsold newspapers = (7*0.5) - (7*0.25) = 1.75
Demanded per day Number of Days Probability Cumulative Probability Random no Class 15 10 0.08 0.08 0 - 0.07 16 20 0.16 0.24 0.08 - 0.23 17 42 0.336 0.58 0.24 - 0.57 18 31 0.248 0.82 0.58 - 0.81 19 12 0.096 0.92 0.82 - 0.91 20 10 0.08 1 0.92 - 0.99 Total 125 1.864 3.64Related Questions
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