- Problem 2.3 (Portfolio management): Hibernia Bank is attempting to determine where its assets should be invested during the current year. At present, $500,000 is available for investment in bonds, home loans, auto loans, and personal loans. The annual rates of return on each type of investment are known to be the following: bonds, 10%; home loans, 16%; auto loans, 13%; and personal loans, 20%. To ensure that the bank's portfolio is not too risky, the bank's investment manager has placed the following three restrictions on the bank's portfolio: The amount invested in personal loans cannot exceed the amount invested in bonds. The amount invested in home loans cannot exceed the amount invested in auto loans. No more than 25% of the total amount invested may be in personal loans. Formulate an LP problem that will maximize the expected return on investment (ROI), solve the problem, and answer each of the following questions. (8 points) (a) What is the optimal allocation of funds to the various investment types? (b) What is your maximum expected return on your $500,000 investment? (e) If the limit on the total amount invested in personal loans were increased to 30%, what would be the improvement in the return on investment? (d) If the return on bonds increases from 10% to 13%, what will happen to the optimal allocation of funds