Answer and explain the following exercises:

1. What are the advantages and limitations of constraint models?

2. What is a Monte Carlo simulation? What principles are the foundation of its application and what steps are followed?

3. The number of cars that arrived per hour at the Lundberg car wash during the last 200 hours of operation was as follows:

Number of cars arriving	Frequency
3 or less	0
4	20
5	30
6	50
7	60
8	40
9 or more	0
	Total 200

Taken from Render, B., Stair, R.M., Hanna, M.E. & Hale, T.S. (2018). Quantitative Analysis For Management. (13 ed.). Pearson.

a. Establish the probability and cumulative probability distributions for the arrival of cars variable.

b. Set the random number ranges for the variable.

c. Simulate 15 hours of car arrivals and calculate the average number of arrivals per hour.

This exercise can be solved with Excel QM or QM for Windows

4. Describe how we can use Markov analysis to make predictions.

5. The University of South Wisconsin has had a stable enrollment for the past five years. The school has its own bookstore, the University Bookstore, but there are also three private bookstores in town: Bill's Book Store, College Bookstore and Battle's Book Store. The university is concerned about the large number of students who are shopping at one of the private bookstores. As a result, South Wisconsin President Andy Lange decided to give a student three hours of college credit to study the problem. The following transition probability matrix was obtained:

University Bill's College Battle's
University	0.6	0.2	0.1	0.1
Bill's	0	0.7	0.2	0.1
College	0.1	0.1	0.8	0
Battle's	0.05	0.05	0.1	0.8

Taken from Render, B., Stair, R.M., Hanna, M.E. & Hale, T.S. (2018). Quantitative Analysis For Management. (13 ed.). Pearson.

a. Currently, each of the four bookstores has an equal share of the market. What will be the market shares for the next period?

This exercise can be solved with Excel QM or QM for Windows