Homework Assignment 3

Exercise 1For the past 50 days, daily sales of Bookstore have been recorded (to the nearest 10).

Units Sold	Number of Times
3	8
4	12
5	15
6	10
7	5

a.Determine the relative and cumulative frequency for each number of units sold.

Units Sold	Number of Times	Relative frequency	Cumulative frequency
3	8
4	12
5	15
6	10
7	5

b.Suppose that the following random numbers were obtained using Excel:

.12 .96 .53 .80 .95 .10 .39 .45 .77 .29

Use these random numbers to simulate 10 days of sales.

Trial	RN	Sales
1	0.12
2	0.96
3	0.53
4	0.80
5	0.95
6	0.10
7	0.39
8	0.45
9	0.77
10	0.29
	Sum

c. Find the average sales?

Exercise2. Hotel California

Hotel LA is a luxury hotel which has just got a new manager, Bob. Given its location and quality, the hotel always had enough people making advance reservations to fill up all the rooms available. The hotel charges $200 per room per night for reservations made in advance (Hint: think of this $200 as the purchasing cost in the Newsvendor model). Bob took classes last semester and decided to implement some of the techniques he learnt in his current job. He implemented a policy of reserving some rooms for last-minute requests and charges these requests $500 per room per night (Hint: think of this $500 as the selling price in the Newsvendor model). The unsold reserved rooms are worth nothing at the end of the day (Hint: that is the salvage value is $0). Based on his estimation, the number of last-minute customers is uniformly distributed with a minimum of 3 and a maximum of 12.

a) How much is the cost of reserving too little by one? That is the underage cost,.

b) How much is the cost of reserving too much by one? That is the overage cost,.

c) What is the optimal service level?

d) How many rooms should be reserved for the last-minute customers? Hint: what is?