Investment Municipal bonds Real estate stocks Pharmaceutical stocks Domestic automobile stocks Projected Rate of Return (%) 5.2 10.5 8.2 8.4 Risk Low High Moderate Moderate QUESTION 1 Topic: an LP application in Portfolio selection (14 marks) A brokerage firm has been tasked with investing $800,000 for a new client with the following guidelines: At least 21% of the total amount invested should be in municipal bonds No more than 50% of the total amount invested should be in real estate stocks. The return from moderate-risk investments must be at least 30% of the return from high-risk investment. At least 12% in pharmaceutical stock. 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. [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 Pharmaceutical stocks investment decreases to 8.0% 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 (%) 5.2 10.5 8.2 8.4 Risk Low High Moderate Moderate QUESTION 1 Topic: an LP application in Portfolio selection (14 marks) A brokerage firm has been tasked with investing $800,000 for a new client with the following guidelines: At least 21% of the total amount invested should be in municipal bonds No more than 50% of the total amount invested should be in real estate stocks. The return from moderate-risk investments must be at least 30% of the return from high-risk investment. At least 12% in pharmaceutical stock. 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. [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 Pharmaceutical stocks investment decreases to 8.0% and all other rates of return are unchanged? Explain. [2]