An established, successful pizza shop owner in NJ has connections to the Clemson area and is considering opening up a branch of their pizzeria in Clemson. It will cost the owner $250,000 to establish this branch. Based on historical data and the quality of NJ pizza, there are three potential outcomes for opening up the branch: (1) the branch is wildly successful because it has figured out how to bring NJ-level pizza to Clemson, (2) the branch is successful since it has brought good pizza to Clemson, and (3) the branch is unsuccessful due to competition from existing pizzerias in Clemson. The first outcome occurs with a probability of .05 and would bring the owner $1,000,000 in profits over the lifetime of the pizzeria. The second outcome occurs with a probability of .50 and would bring the owner $500,000 in profits over the lifetime of the pizzeria. The third outcome occurs with a probability of .45 and would cause losses of an additional $100,000 over the lifetime of the pizzeria. The owner must choose between opening the pizzeria or not. (a) Develop a decision analysis formulation of this problem by identifying the decision alternatives, the states of nature, and the payoff table. b) What decision would the owner implement according to Bayes rule? (c) What is the range of additional losses that could occur in Outcome 3 that would keep the decision from (b) optimal?

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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Please do this with hand written work An established, successful pizza shop owner in NJ has connections to the Clemson area and is considering opening up a branch of their pizzeria in Clemson. It will cost the owner $250,000 to establish this branch. Based on historical data and the quality of NJ pizza, there are three potential outcomes for opening up the branch: (1) the branch is wildly successful because it has figured out how to bring NJ-level pizza to Clemson, (2) the branch is successful since it has brought good pizza to Clemson, and (3) the branch is unsuccessful due to competition from existing pizzerias in Clemson. The first outcome occurs with a probability of .05 and would bring the owner $1,000,000 in profits over the lifetime of the pizzeria. The second outcome occurs with a probability of .50 and would bring the owner $500,000 in profits over the lifetime of the pizzeria. The third outcome occurs with a probability of .45 and would cause losses of an additional $100,000 over the lifetime of the pizzeria. The owner must choose between opening the pizzeria or not. (a) Develop a decision analysis formulation of this problem by identifying the decision alternatives, the states of nature, and the payoff table. b) What decision would the owner implement according to Bayes rule? (c) What is the range of additional losses that could occur in Outcome 3 that would keep the decision from (b) optimal?

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