A car agency has offices in Phoenix, Denver and Chicago. The agency allows one- or two-way rentals so that cars rented in one location may end up in another. Statistics show that at the end of each week 70% of all rentals are twoway. As for the one-way rentals: from Phoenix, 40% go to Denver, and the rest to Chicago; from Denver, 60% go to Chicago and the rest to Phoenix; from Chicago, 40% go to Denver and the rest to Phoenix; (a) Express the situation as s Markov chain. (b) If the agency starts the week with 100 cars in each location, what will the distribution be like in two weeks (two-step transition probability matrix)? (c) If each location is designed to handle a maximum of 120 cars, would there be a long run space availability problem in any of the location?

A car agency has offices in Phoenix, Denver and Chicago. The agency allows one- or two-way rentals so that cars rented in one location may end up in another. Statistics show that at the end of each week 70% of all rentals are twoway. As for the one-way rentals: from Phoenix, 40% go to Denver, and the rest to Chicago; from Denver, 60% go to Chicago and the rest to Phoenix; from Chicago, 40% go to Denver and the rest to Phoenix; (a) Express the situation as s Markov chain. (b) If the agency starts the week with 100 cars in each location, what will the distribution be like in two weeks (two-step transition probability matrix)? (c) If each location is designed to handle a maximum of 120 cars, would there be a long run space availability problem in any of the location?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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