Maximizing Investment Returns w/ Linear Programming

In summary, an investment group has $250,000 to invest with specific requirements for their portfolio. The portfolio must include at least 20% in municipal bonds, at least 40% in a combination of electronic, aerospace, and drug firms, and no more than 50% of municipal bonds in a high-risk nursing home stock. The brokerage has recommended specific investments, including Los Angeles municipal bonds, Thompson Electronics, Inc., United Aerospace Corp, Palmer Drugs, and Happy Days Nursing Home. A linear programming problem has been set up to maximize the rate of return while following the investment requirements.
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TiburonSangre
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Homework Statement



An investment group has $250,000 to invest. At least 20% must be in municipal bonds, at least 40% in a combination of (electronic firms, aerospace firms, & drug manufacturers), & finally no more than 50% in municipal bonds should be placed in a high-risk, high yield nursing home stock.

The brokerage came up with these investments

Investment Percentage Rate of Return
(%)

Los Angeles municipal bonds 5.3
Thompson Electronics, Inc 6.8
United Aerospace Corp 4.9
Palmer Drugs 8.4
Happy Days Nursing Home 11.8



Homework Equations


5.3X1 + 6.8X2 + 4.9X3 + 8.4X4 + 11.8X5 = maximized
X1 < or = 50000
X2 + X3 + X4 < or = 100000
X5 > or = 125000


The Attempt at a Solution

 
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5.3X1 + 6.8X2 + 4.9X3 + 8.4X4 + 11.8X5 = maximized X1 + X2 + X3 + X4 + X5 = 250000 X1 < or = 50000X2 + X3 + X4 < or = 100000 X5 > or = 125000 Set up a linear programming problem Maximize 5.3X1 + 6.8X2 + 4.9X3 + 8.4X4 + 11.8X5 Subject to X1 + X2 + X3 + X4 + X5 = 250000X1 < or = 50000X2 + X3 + X4 < or = 100000X5 > or = 125000X1, X2, X3, X4, X5 > or = 0
 

Related to Maximizing Investment Returns w/ Linear Programming

1. What is linear programming?

Linear programming is a mathematical optimization technique used to find the best possible solution for a given problem with linear constraints. It involves maximizing or minimizing a linear objective function while satisfying a set of linear constraints.

2. How can linear programming be applied to maximizing investment returns?

Linear programming can be used to determine the optimal allocation of resources in order to maximize investment returns. By setting up a linear programming model with decision variables representing different investment options and constraints such as budget limits and risk tolerance, an optimal solution can be found that maximizes the return on investment.

3. What are the benefits of using linear programming for investment optimization?

Using linear programming for investment optimization allows for a systematic and objective approach to decision making. It also takes into account multiple constraints and factors, such as budget limits and risk tolerance, which can be difficult to consider manually. Additionally, it can help identify the most efficient use of resources to achieve the desired investment returns.

4. Are there any limitations to using linear programming for investment optimization?

Linear programming is based on certain assumptions and may not always accurately reflect real-world scenarios. It also requires accurate and reliable data inputs to produce meaningful results. Furthermore, linear programming models may become complex and difficult to solve for larger and more complex investment portfolios.

5. What are some real-world applications of linear programming for investment optimization?

Linear programming is widely used in the financial industry for portfolio optimization, asset allocation, and risk management. It is also used in other industries such as transportation and logistics for route optimization and resource allocation. Additionally, it can be applied to various decision-making problems in business and engineering.

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