A bank makes four kinds of loans to its personal customers, and these loans yield the following interest rates: Home improvement 3.5%, First mortgage 3%, Second mortgage 4%, Personal overdraft 5%. The bank has a maximum lending capability of 250 million, and is further con- strained by the following policies: First mortgages must be at least 65% of all mortgages issued, and at least 25% of all loans issued (in monetary terms); second mortgages cannot exceed 20% of all loans issued (in monetary terms); to avoid bad publicity and the threat of additional taxation (through a windfall tax), the average interest rate on all loans must not exceed 4%. a) Formulate the banks loan problem as a Linear Program so as to maximise the interest income whilst satisfying the above constraints. b) Solve the problem to find an optimal allocation of funds between the loan types.

c) Do you think this optimal solution is unique? Explain your reasoning.