c) A winner of the MS Lotto has decided to invest $50,000 per year in the stock market. Under consideration are stocks for a petrochemical firm and a public utility. Although a long-range goal is to get the highest possible return, some consideration is given to the risk involved with the stocks. A risk index on a scale of 1-10 (with 10 being the riskiest) is assigned to each of the two stocks. The total risk of the portfolio is found by multiplying the risk of each stock by the dollars invested in that stock. The following table provides a summary of the return and risk: Stock Estimated Return Petrochemical 12% Utility 6% Risk Index 9 4 The investor would like to maximize the return on the investment, but the average risk index of the investment should not be higher than 6. (i) Formulate an LP model for this problem. (3 marks) (ii) Sketch the feasible region for this problem. (4 marks) (iii) Estimate the return for this investment. (3 marks) Suppose the investor has changed his attitude about the investment and wishes to give greater emphasis to the risk of the investment. Now the investor wishes to minimize the risk of the investment as long as a return of at least 8% is generated. (i) Formulate an LP model for this problem. (3 marks) Page 1 of 4 BB 203 Group Assignment Sep-Dec 2020 (ii) Sketch the feasible region for this problem. (iii) Estimate the return for this re-investment. (4 marks) (3 marks) c) A winner of the MS Lotto has decided to invest $50,000 per year in the stock market. Under consideration are stocks for a petrochemical firm and a public utility. Although a long-range goal is to get the highest possible return, some consideration is given to the risk involved with the stocks. A risk index on a scale of 1-10 (with 10 being the riskiest) is assigned to each of the two stocks. The total risk of the portfolio is found by multiplying the risk of each stock by the dollars invested in that stock. The following table provides a summary of the return and risk: Stock Estimated Return Petrochemical 12% Utility 6% Risk Index 9 4 The investor would like to maximize the return on the investment, but the average risk index of the investment should not be higher than 6. (i) Formulate an LP model for this problem. (3 marks) (ii) Sketch the feasible region for this problem. (4 marks) (iii) Estimate the return for this investment. (3 marks) Suppose the investor has changed his attitude about the investment and wishes to give greater emphasis to the risk of the investment. Now the investor wishes to minimize the risk of the investment as long as a return of at least 8% is generated. (i) Formulate an LP model for this problem. (3 marks) Page 1 of 4 BB 203 Group Assignment Sep-Dec 2020 (ii) Sketch the feasible region for this problem. (iii) Estimate the return for this re-investment. (4 marks)
