The esteemed brokerage firm of Black, Scholes and Merton has just been instructed by one of its clients to invest $250,000 of her money obtained recently through the sale of Netflix, Inc. The client has a good deal of trust in the brokerage firm, but she also has her own ideas about the distribution of the funds being invested. In particular, she requests that the firm select whatever stocks and bonds they believe are well rated, but within the following guidelines: 1. Municipal bonds should constitute at least 20% of the investment 2. At least 40% of the funds should be placed in a combination of electronic firms, airline firms and drug manufacturers 3. No more than 50% of the amount invested in municipal bonds should be placed in a high risk, high yield nursing home stock. Subject to these constraints, the clients goal is to maximize projected return on investment. The firm of Black, Scholes and Merton, aware of these guidelines, prepare a list of high quality stocks and bonds and their corresponding rates of return: Investment Projected Rate of Return (%) Bruderheim municipal bonds 5.3 SAMU Electronics 6.8 Westplane Airlines 4.9 Trudeau Drugs 8.4 Happy Days Nursing Homes 11.8 a. Formulate the problem algebraically a linear programming model for this problem. (5 marks) b. Solve this problem using Excel. (5 marks)