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