A 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 rate of return on each type of investment is known to be: bonds, 10%; home loans, 16%; auto loans, 13%; personal loans, 20%. To ensure that the bank's portfolio is not too risky, the invest manager has developed the following restrictions: 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. (a) The bank's objective is to maximize annual return on its investments. Formulate a LP that will enable the bank to meet this objective. (b) Is a linear program appropriate for modeling this scenario? Answer this question by performing a critique of your model against the four main assumptions of linear programming.