Essentials Of Business Analytics
1st Edition
ISBN: 9781285187273
Author: Camm, Jeff.
Publisher: Cengage Learning,
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Chapter 9, Problem 9P
Galaxy Cloud Services operates several data centers across the United States containing servers that store and process the data on the Internet. Suppose that Galaxy Cloud Services currently has five outdated data centers: one each in Michigan, Ohio, and California and two in New York. Management is considering increasing the capacity of these data centers to keep up with increasing demand. Each data center contains servers that are dedicated to Secure data and to Super Secure data. The cost to update each data center and the resulting increase in server capacity for each type of server are as follows:
The projected needs are for a total increase in capacity of 90 Secure servers and 90 Super Secure servers. Management wants to determine which data centers to update to meet projected needs and, at the same time, minimize the total cost of the added capacity.
- a. Formulate a binary integer programming model that could be used to determine the optimal solution to the capacity increase question facing management.
- b. Solve the model formulated in part (a) to provide a recommendation for management.
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1- Let A = {A1, A2, ...), in which A, A, = 0, when i j.
a) Is A a π-system? If not, which element(s) should be added to A to become a π-system?
b) Prove that σ(A) consists of the finite or countable unions of elements of A; i.c., A E σ(A) if and
only if there exists finite or countable sequence {n} such that A = U₁An (Hint: Let F be such
class; prove that F is a σ-filed containing A.)
c) Let p ≥ 0 be a sequence of non-negative real numbers with Σip₁ = 1. Using p₁'s, how do you
construct a probability measure on σ(A)? (Hint: use extension theorem.)
2- Construct an example for which P(lim sup A,) = 1 and P(lim inf An) = 0.
In a town with 5000 adults, a sample of 50 is selected using SRSWOR and asked their opinion of a proposed municipal project; 30 are found to favor it and 20 oppose it. If, in fact, the adults of the town were equally divided on the proposal, what would be the probability of observing what has been observed? Approximate using the Binomial distribution. Compare this with the exact probability which is 0.0418.
Chapter 9 Solutions
Essentials Of Business Analytics
Ch. 9 - STAR Co. provides paper to smaller companies with...Ch. 9 - The following questions refer to a capital...Ch. 9 - Spencer Enterprises is attempting to choose among...Ch. 9 - Hawkins Manufacturing Company produces connecting...Ch. 9 - Grave City is considering the relocation of...Ch. 9 - Hart Manufacturing makes three products. Each...Ch. 9 - Galaxy Cloud Services operates several data...Ch. 9 - East Coast Trucking provides service from Boston...
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