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An investment company manages portfolios of stocks, bonds, and other investment alternatives. One of the company's clients would like to invest $200,000 in stocks. The client is interested in four specific stocks - A, B, C, and/or D. The company gathered the following relevant financial data for the four stocks: Stock C Stock A Stock B Stock D Price per share Annual rate of $100 0.12 $50 S80 $40 0.08 0.06 0.10 return Risk measure 0.10 0.07 0.05 0.08 per dollar invested Based on the above data, the investor has stipulated the following investment guidelines: 1. The entire amount of $200,000 must be invested. 2. The annual rate of return must be at least 9% of the invested capital of $200,000. 3. Not every stock has to be purchased, however, if selected, no one stock can account for more than 50% of the total dollar investment. 4. The total investment in stocks A and B combined must be equal to or greater than the total investment in stocks C and D combined.

An investment company manages portfolios of stocks, bonds, and other investment alternatives. One of the company's clients would like to invest $200,000 in stocks. The client is interested in four specific stocks - A, B, C, and/or D. The company gathered the following relevant financial data for the four stocks: Stock C Stock A Stock B Stock D Price per share Annual rate of $100 0.12 $50 S80 $40 0.08 0.06 0.10 return Risk measure 0.10 0.07 0.05 0.08 per dollar invested Based on the above data, the investor has stipulated the following investment guidelines: 1. The entire amount of $200,000 must be invested. 2. The annual rate of return must be at least 9% of the invested capital of $200,000. 3. Not every stock has to be purchased, however, if selected, no one stock can account for more than 50% of the total dollar investment. 4. The total investment in stocks A and B combined must be equal to or greater than the total investment in stocks C and D combined.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Q1. Build a linear programming model to develop an investment portfolio that minimizes total risk under the above constraints.

 

  1. a) Define the decision making variables.
  2. b) Show the objective function.
  3. c) Show the constraints.
An investment company manages portfolios of stocks, bonds, and other investment alternatives. One of the company's clients would like to invest $200,000 in stocks. The client is interested in four specific stocks - A, B, C, and/or D. The company gathered the following relevant financial data for the four stocks: Stock C Stock A Stock B Stock D Price per share S100 $50 S80 $40 Annual rate of 0.12 0.08 0.06 0.10 return Risk measure 0.10 0.07 0.05 0.08 per dollar invested Based on the above data, the investor has stipulated the following investment guidelines: 1. The entire amount of $200,000 must be invested. 2. The annual rate of return must be at least 9% of the invested capital of $200,000. 3. Not every stock has to be purchased, however, if selected, no one stock can account for more than 50% of the total dollar investment. 4. The total investment in stocks A and B combined must be equal to or greater than the total investment in stocks C and D combined.
Transcribed Image Text:An investment company manages portfolios of stocks, bonds, and other investment alternatives. One of the company's clients would like to invest $200,000 in stocks. The client is interested in four specific stocks - A, B, C, and/or D. The company gathered the following relevant financial data for the four stocks: Stock C Stock A Stock B Stock D Price per share S100 $50 S80 $40 Annual rate of 0.12 0.08 0.06 0.10 return Risk measure 0.10 0.07 0.05 0.08 per dollar invested Based on the above data, the investor has stipulated the following investment guidelines: 1. The entire amount of $200,000 must be invested. 2. The annual rate of return must be at least 9% of the invested capital of $200,000. 3. Not every stock has to be purchased, however, if selected, no one stock can account for more than 50% of the total dollar investment. 4. The total investment in stocks A and B combined must be equal to or greater than the total investment in stocks C and D combined.
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