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An investor is considering three types of investments: a high risk venture into oil leases with a potential return of 15%, a medium risk investment in bonds with a 9% return, and a relatively safe stock investment with a 5% return. He has $50,000 to invest. Because of the risk, he will limit his investments in oil leases and bonds to 30% and his investments in oil leases and stock to 50%. How much should he invest in each to maximize his return, assuming investment returns are as expected? a. Define the variables b. Clearly state the constraints (all inequalities) related to the feasible region c. State the objective function

An investor is considering three types of investments: a high risk venture into oil leases with a potential return of 15%, a medium risk investment in bonds with a 9% return, and a relatively safe stock investment with a 5% return. He has $50,000 to invest. Because of the risk, he will limit his investments in oil leases and bonds to 30% and his investments in oil leases and stock to 50%. How much should he invest in each to maximize his return, assuming investment returns are as expected? a. Define the variables b. Clearly state the constraints (all inequalities) related to the feasible region c. State the objective function

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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An investor is considering three types of investments: a high risk venture into oil leases with a potential return of 15%, a medium risk investment in bonds with a 9% return, and a relatively safe stock investment with a 5% return. He has $50,000 to invest. Because of the risk, he will limit his investments in oil leases and bonds to 30% and his investments in oil leases and stock to 50%. How much should he invest in each to maximize his return, assuming investment returns are as expected? a. Define the variables b. Clearly state the constraints (all inequalities) related to the feasible region c. State the objective function d. Set up the initial simplex matrix needed to solve the linear programming problem using the Simplex Method e. Perform all pivots necessary using row operations to transform the matrix until the solution is feasible f. How much should he invest in each to maximize his return, assuming investment returns are as expected?
Transcribed Image Text:An investor is considering three types of investments: a high risk venture into oil leases with a potential return of 15%, a medium risk investment in bonds with a 9% return, and a relatively safe stock investment with a 5% return. He has $50,000 to invest. Because of the risk, he will limit his investments in oil leases and bonds to 30% and his investments in oil leases and stock to 50%. How much should he invest in each to maximize his return, assuming investment returns are as expected? a. Define the variables b. Clearly state the constraints (all inequalities) related to the feasible region c. State the objective function d. Set up the initial simplex matrix needed to solve the linear programming problem using the Simplex Method e. Perform all pivots necessary using row operations to transform the matrix until the solution is feasible f. How much should he invest in each to maximize his return, assuming investment returns are as expected?
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