OECS Bank has both a loans division and mutual funds division. It has allocated $40.0M to finance its loan portfolio. Its operations manager is asked to build an LP model to help guide company decisions as to how to disburse the revolving fund across different loan categories. The operations manager garnered the following data on available types of loans based on market research of the industry: Types of loan Interest rate Bad debt ratio Personal 0.15 .10 Car 0.20 0.04 Home 0.17 0.02 Small and medium enterprises 0.25 0.15 Commercial 0.10 0.02 The Bank's net return is interest rate net of Bad debt. Revenue from interst is gained only from good loans. The mutual funds Division has allocated $5.0M and is currently looking for investment opportunities to invest these funds. The financial analyst suggested that all new investments be made in the oil industry, steel industry or in government bonds. The analyst identified five investment opportunities: two from the oil industry, two from the steel and government bonds. Types of opportunities Returns ABC oil 0.095 XZY oil 0.085 Mona steel 0.04 TNT steel 0.05 Government Bonds 0.015 Formulate a LP model for the OECS bank that will maximize net returns from the loans division and a separate model for the Mutual Funds Division including ratio constraints. For the Loan portfolio (8 marks): a) Generate the objective function using your variables from above(2 marks) b) Generate the total budget constraint(1 mark) c) The bank allocates at least 45% of the funds to SMEs and Commercial loans. (1 mark) d) Home loans must equal at least 50% of the personal, car and homes loans.(2 marks e) The bank also has a stated policy of not allowing the overall ratio of bad debts on all loans to exceed 5 %. (1.5 marks) g) Generate the non-negative constraint (.5 mark) I For the mutual Funds Division (12 marks): a) Generate the objective function (2 marks) b) Generate the budget constraint (1 mark) c) The amount invested in oil should be at least three times the amount invested in the steel industry (1:5 mark d) The investment in ABC oil cannot be more than 50% of total oil industry (1.5 mark) e) The investment in TNT steel should be at most 40 % of the total investment in Government Bond (15 mark) f) The investment in XYZ oil should be at least 20 % of the total funds available but no more than 40% of total funds (1.5 mark) g) The steel industry should not receive more than 30 % of total funds (1.5 mark)