QUESTION 1 Topic: an LP application in Portfolio selection (14 marks)

A brokerage firm has been tasked with investing $650,000 for a new client with the following guidelines:

At least 20% of the total amount invested should be in municipal bonds

At least 11% in pharmaceutical stocks.

No more than 65% of the total amount invested should be in real estate stocks and pharmaceutical stocks.

At least 13% in domestic automobile stocks

The clients goal is to maximize the return on investments.

The broker has prepared a list of high-quality stocks and bonds and their corresponding rates of returnas shown in the table above.

1) Formulate a linear programming model for this problem. Clearly define the variables, objective function, and constraints. [5]

2) Solve the problem using Excel or Excel QM and answer the following questions:

a) What is the optimal solution to this LP problem? [7]

b) Would the optimal solution change if the rate of return from Municipal bonds investment increases to 6% and all other rates of return are unchanged? Explain. [2]

Investment	Projected Rate of Return (%)	Risk
Municipal bonds	5.7	Low
Real estate stocks	10	High
Pharmaceutical stocks	8.1	Moderate
Domestic automobile stocks	8.5	Moderate

Investment Municipal bonds Real estate stocks Pharmaceutical stocks Domestic automobile stocks Projected Rate of Return (%) 5.7 e 10 8.1 8.5 Risk Low High Moderate Moderate QUESTION 1 Topic: an LP application in Portfolio selection (14 marks) A brokerage firm has been tasked with investing $650,000 for a new client with the following guidelines: At least 20% of the total amount invested should be in municipal bonds At least 11% in pharmaceutical stocks. No more than 65% of the total amount invested should be in real estate stocks and pharmaceutical stocks. At least 13% in domestic automobile stocks The client's goal is to maximize the return on investments. The broker has prepared a list of high-quality stocks and bonds and their corresponding rates of return as shown in the table above. 1) Formulate a linear programming model for this problem. Clearly define the variables, objective function, and constraints. 151 2) Solve the problem using Excel or Excel QM and answer the following questions: I a) What is the optimal solution to this LP problem? [7] b) Would the optimal solution change if the rate of return from Municipal bonds investment increases to 6% and all other rates of return are unchanged? Explain. [2] Investment Municipal bonds Real estate stocks Pharmaceutical stocks Domestic automobile stocks Projected Rate of Return (%) 5.7 e 10 8.1 8.5 Risk Low High Moderate Moderate QUESTION 1 Topic: an LP application in Portfolio selection (14 marks) A brokerage firm has been tasked with investing $650,000 for a new client with the following guidelines: At least 20% of the total amount invested should be in municipal bonds At least 11% in pharmaceutical stocks. No more than 65% of the total amount invested should be in real estate stocks and pharmaceutical stocks. At least 13% in domestic automobile stocks The client's goal is to maximize the return on investments. The broker has prepared a list of high-quality stocks and bonds and their corresponding rates of return as shown in the table above. 1) Formulate a linear programming model for this problem. Clearly define the variables, objective function, and constraints. 151 2) Solve the problem using Excel or Excel QM and answer the following questions: I a) What is the optimal solution to this LP problem? [7] b) Would the optimal solution change if the rate of return from Municipal bonds investment increases to 6% and all other rates of return are unchanged? Explain. [2]