First Securities, Inc., an investment firm, has $380,000 on account. The chief investment officer would like to reinvest the $380,000 in a portfolio that would maximize return on investment while at the same time maintaining a relatively conservative mix of stocks and bonds. The following table shows the investment opportunities and rates of return.
Investment Opportunity Rate of Return
Municipal Bonds 0.095
High Tech Stock 0.146
Blue Chip Stock 0.075
Federal Bonds 0.070
The Board of Directors has mandated that at least 60 percent of the investment consist of a combination of municipal and federal bonds, 25 percent Blue Chip Stock, and no more than 15 percent High Tech Stock.
(a) Formulate this portfolio selection problem using linear programming.
(b) Solve using LP software such as Excel QM or QM for windows. Write out answer step by step if you can't use QM.
This solution creates a linear program to formulate the selection problem and shows step-by-step calculations to determine municipal bonds, high tech stock, blue chip stock, federal bond and total returns on investment.