2. Balanced Bank [BB] has both corporate and personal lending customers. On average, the profit contribution margin or interest rate spread is 1.75% on corporate loans and 2.25% on personal loans. This return difference reflects the fact that personal loans tend to be riskier than corporate loans. BB seeks to maximize the total dollar profit contribution earned, subject to a variety of restrictions on their lending practices. In order to limit default risk, BB must restrict personal loans to no more than 40% of total loans outstanding. Similarly, to ensure adequate diversification against business cycle risk, corporate lending cannot exceed 80% of loaned funds. To maintain good customer relations by serving the basic needs of the local business community, BB has decided to extend at least 40% of total credit authorization to corporate customers on an ongoing basis. Finally, BB cannot exceed their current total credit authorization of $50 million. a. Set up and interpret the linear programming problem BB would use to determine the optimal dollar amount of credit in corporate (C) and personal (P) lending customers. Write both the inequality and equality forms of the constraint conditions. b. Use a graph to determine the optimal solution and check your answer algebraically. Please be neat and show and label the constraints and show and label at least one isoreturn line on your graph. Interpret the solution. Be sure to discuss which constraints are binding or slack and by how much. Holding all else equal, how much would the average profit contribution margin on corporate loans have to rise before the optimal investment policy determined in part A would change? Explain briefly. C. 2. Balanced Bank [BB] has both corporate and personal lending customers. On average, the profit contribution margin or interest rate spread is 1.75% on corporate loans and 2.25% on personal loans. This return difference reflects the fact that personal loans tend to be riskier than corporate loans. BB seeks to maximize the total dollar profit contribution earned, subject to a variety of restrictions on their lending practices. In order to limit default risk, BB must restrict personal loans to no more than 40% of total loans outstanding. Similarly, to ensure adequate diversification against business cycle risk, corporate lending cannot exceed 80% of loaned funds. To maintain good customer relations by serving the basic needs of the local business community, BB has decided to extend at least 40% of total credit authorization to corporate customers on an ongoing basis. Finally, BB cannot exceed their current total credit authorization of $50 million. a. Set up and interpret the linear programming problem BB would use to determine the optimal dollar amount of credit in corporate (C) and personal (P) lending customers. Write both the inequality and equality forms of the constraint conditions. b. Use a graph to determine the optimal solution and check your answer algebraically. Please be neat and show and label the constraints and show and label at least one isoreturn line on your graph. Interpret the solution. Be sure to discuss which constraints are binding or slack and by how much. Holding all else equal, how much would the average profit contribution margin on corporate loans have to rise before the optimal investment policy determined in part A would change? Explain briefly. C
