Question #1: Linear Programming Model Formulation Sami is to invest up to $10 million in three investment funds: a stock fund, oil market fund, interest fund, and retirement fund. The stock fund provides an annual rate of return of 12%; the oil market fund provides an annual rate of return of 10%; the interest fund provides an annual rate of return of 6%, and the retirement fund provides an annual rate of return of 4%. Sami wants at least $1 million be invested in each fund. Further, the amount invested in the any fund shall not exceed 50% of the amount invested in the other three funds. Investment in the stock fund, oil market, interest, and retirement funds have risk rating of 10, 8, 5 and 2 per thousand dollars respectively. Formulate a linear programming model (objective function and constraint equations) that can be used to determine the amount of money to invest in each fund for each of the following cases: Question 4: Expected Value of Sample Information Assume that Tabuk Housing Corporation's management, in Question #1, is considering a market research study designed to learn more about potential market acceptance of the housing project. Management anticipates that the market research study will provide one of the following two results: 1. Favorable report: A significant number of the individuals' contacted express interest in the housing project. 2. Unfavorable report: Very few of the individuals' contacted express interest in the housing project. If the market research study is undertaken: P(Favorable report)=0.9 P(Unfavorable report) = 0.1 If the market research report is favorable: P (Strong demand given a favorable report)=0.7 P (Moderate demand given a favorable report)=0.2 P (Weak demand given a favorable report)=0.1 If the market research report is unfavorable: P (Strong demand given a unfavorable report)=0.2 P (Moderate demand given a unfavorable report)=0.35 P (Weak demand given a unfavorable report)=0.45 If the market research report is not undertaken, the prior probabilities are applicable: P (Strong demand) 0.5 P (Moderate demand)=0.3 P (Weak demand)=0.2 Answer the Following Questions: A) Draw the Decision Tree showing the probabilities and payoffs. B) Calculate the expected values of each decision. C) Select the optimal decision strategy if the market research is favorable.

Question #1: Linear Programming Model Formulation Sami is to invest up to $10 million in three investment funds: a stock fund, oil market fund, interest fund, and retirement fund. The stock fund provides an annual rate of return of 12%; the oil market fund provides an annual rate of return of 10%; the interest fund provides an annual rate of return of 6%, and the retirement fund provides an annual rate of return of 4%. Sami wants at least $1 million be invested in each fund. Further, the amount invested in the any fund shall not exceed 50% of the amount invested in the other three funds. Investment in the stock fund, oil market, interest, and retirement funds have risk rating of 10, 8, 5 and 2 per thousand dollars respectively. Formulate a linear programming model (objective function and constraint equations) that can be used to determine the amount of money to invest in each fund for each of the following cases: Question 4: Expected Value of Sample Information Assume that Tabuk Housing Corporation's management, in Question #1, is considering a market research study designed to learn more about potential market acceptance of the housing project. Management anticipates that the market research study will provide one of the following two results: 1. Favorable report: A significant number of the individuals' contacted express interest in the housing project. 2. Unfavorable report: Very few of the individuals' contacted express interest in the housing project. If the market research study is undertaken: P(Favorable report)=0.9 P(Unfavorable report) = 0.1 If the market research report is favorable: P (Strong demand given a favorable report)=0.7 P (Moderate demand given a favorable report)=0.2 P (Weak demand given a favorable report)=0.1 If the market research report is unfavorable: P (Strong demand given a unfavorable report)=0.2 P (Moderate demand given a unfavorable report)=0.35 P (Weak demand given a unfavorable report)=0.45 If the market research report is not undertaken, the prior probabilities are applicable: P (Strong demand) 0.5 P (Moderate demand)=0.3 P (Weak demand)=0.2 Answer the Following Questions: A) Draw the Decision Tree showing the probabilities and payoffs. B) Calculate the expected values of each decision. C) Select the optimal decision strategy if the market research is favorable.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section5.5: Shortest Path Models

Problem 32P

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