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.   _____

Answer 1

Newspapers demanded per day	Number of Days	Probability	Cumulative Probability	Random no. ranges
15	10	0.08	0.08	0.00 - 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	1.00	0.92 - 0.99

--------------------

Day	Demand	Random Number	Quantity Ordered	Sales	Unsatisfied Demand	Unsold Papers
1	18	0.78	18	18	0	0
2	17	0.43	18	17	0	1
3	20	0.93	17	17	3	0
4	19	0.87	20	19	0	1
5	17	0.48	19	17	0	2
6	19	0.84	17	17	2	0
7	19	0.87	19	19	0	0
8	17	0.27	19	17	0	2
9	16	0.20	17	16	0	1
10	17	0.52	16	16	1	0
Totals	179		180	173	6	7

12.

Total revenue = 173 x $1 = $173

13.

Loss due to unsold papers = 7 x $0.25 = $1.75
Loss due to unmet demand (opportunity loss) = 6 x ($1 - $0.5) = $3

So, total loss = $4.75