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Task 2: (22 marks) An investment firm is looking for new opportunity to invest up to 4 million dollars in international shares, CO2 futures, gold and Australian governmental bonds. Suppose that the annual return on the investment in the international shares is 3%, CO2 futures is 2%, gold is 1.5%, and the Australian governmental bonds is 1.8% In anticipation of financial markets' rebound, the company's management imposed the following recommendations: The international shares and CO2 futures must not receive more than 60% of the total investment; Investment in CO2 futures and gold must not exceed 2 million dollars; No more than 25% of the total amount invested in CO2 futures and the Australian governmental bonds can be invested into the international shares; Investment amount in the Australian governmental bonds should NOT be more than 40% of the investment in CO2 futures and gold - a) Based on the information above, define relevant decision variables and formulate a linear program to maximize the total annual return on the investment portfolio. b) Use Excel Solver to solve the LP formed above and obtain the results including Answer and Sensitivity reports. May need to refer to one or both of these reports to answer the following questions. i. Show the Answer and Sensitivity reports that you obtained from solving the LP formulation in Excel ii. What is the optimal value of the objective function under the optimal investment plan/solution? Solver, by inserting both reports here via 'copy and paste'. (must show how to calculate it using optimal solutions for the decision variables). ii. What is the total amount of money to be invested under the optimal investment plan? iv. v. How much can be invested in CO2 futures and gold according to the optimal investment plan? The management of the company wants to limit the combined investment in CO2 futures and gold to 1 million dollars. Explain clearly how this resolution will affect the optimal investment plan and the objective function value. The senior management has decided to release some of the available total investment fund to train staff in Workplace Health and Safety (WHS). Calculate the amount of money that can be released for WHS training given that the management now has only $3 950 000 available for investment. What is the annual return on the optimal portfolio expressed as a percentage? vi. vii. Task 2: (22 marks) An investment firm is looking for new opportunity to invest up to 4 million dollars in international shares, CO2 futures, gold and Australian governmental bonds. Suppose that the annual return on the investment in the international shares is 3%, CO2 futures is 2%, gold is 1.5%, and the Australian governmental bonds is 1.8% In anticipation of financial markets' rebound, the company's management imposed the following recommendations: The international shares and CO2 futures must not receive more than 60% of the total investment; Investment in CO2 futures and gold must not exceed 2 million dollars; No more than 25% of the total amount invested in CO2 futures and the Australian governmental bonds can be invested into the international shares; Investment amount in the Australian governmental bonds should NOT be more than 40% of the investment in CO2 futures and gold - a) Based on the information above, define relevant decision variables and formulate a linear program to maximize the total annual return on the investment portfolio. b) Use Excel Solver to solve the LP formed above and obtain the results including Answer and Sensitivity reports. May need to refer to one or both of these reports to answer the following questions. i. Show the Answer and Sensitivity reports that you obtained from solving the LP formulation in Excel ii. What is the optimal value of the objective function under the optimal investment plan/solution? Solver, by inserting both reports here via 'copy and paste'. (must show how to calculate it using optimal solutions for the decision variables). ii. What is the total amount of money to be invested under the optimal investment plan? iv. v. How much can be invested in CO2 futures and gold according to the optimal investment plan? The management of the company wants to limit the combined investment in CO2 futures and gold to 1 million dollars. Explain clearly how this resolution will affect the optimal investment plan and the objective function value. The senior management has decided to release some of the available total investment fund to train staff in Workplace Health and Safety (WHS). Calculate the amount of money that can be released for WHS training given that the management now has only $3 950 000 available for investment. What is the annual return on the optimal portfolio expressed as a percentage? vi. vii

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