B-1. As a side business, Mr Happy, keeps a fleet of luxury limousines that he rents out to a few individual clients. Each client needs at most 1 limo. The demand per week (i.e., the total number of customers per week) for Mr Happy's limos has the following probability distribution: Demand/Week 0 1 2 3 4 Probability 0.05 0.2 0.5 0.2 0.05 (a) What is the expected value and the variance of the demand per week?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
B-1. As a side business, Mr Happy, keeps a fleet of luxury limousines that he rents out to a
few individual clients. Each client needs at most 1 limo. The demand per week (i.e., the total
number of customers per week) for Mr Happy's limos has the following probability
distribution:
Demand/Week 0
1
2
4
Probability
0.05
0.2
0.5
0.2
0.05
(a) What is the expected value and the variance of the demand per week?
(b) Suppose Mr. Happy has only 3 limos. It costs Mr. Happy £3,000 per week to maintain
each limousine and his rental price per limo per week is £4,000. What is his expected weekly
profit?
(c) What is the probability that Mr. Happy makes a profit in a randomly chosen week?
(d) Now suppose that you want to enter this business with the same demand distribution as
Mr. Happy. You have to decide how many limos you want to own to maximize your
expected profit. The cost of maintaining each limo and the rental price is the same as Mr.
Happy. How many limos should you own?
Transcribed Image Text:B-1. As a side business, Mr Happy, keeps a fleet of luxury limousines that he rents out to a few individual clients. Each client needs at most 1 limo. The demand per week (i.e., the total number of customers per week) for Mr Happy's limos has the following probability distribution: Demand/Week 0 1 2 4 Probability 0.05 0.2 0.5 0.2 0.05 (a) What is the expected value and the variance of the demand per week? (b) Suppose Mr. Happy has only 3 limos. It costs Mr. Happy £3,000 per week to maintain each limousine and his rental price per limo per week is £4,000. What is his expected weekly profit? (c) What is the probability that Mr. Happy makes a profit in a randomly chosen week? (d) Now suppose that you want to enter this business with the same demand distribution as Mr. Happy. You have to decide how many limos you want to own to maximize your expected profit. The cost of maintaining each limo and the rental price is the same as Mr. Happy. How many limos should you own?
Expert Solution
steps

Step by step

Solved in 4 steps

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman