Financial planning A bank makes four kinds of loans to its personal customers and these loans yield the following annual interest rates to the bank: First mortgage 14% Second mortgage 20% Home improvement 20% Personal overdraft 10% The bank has a maximum foreseeable lending capability of 250 million and is further constrained by the policies: 1. first mortgages must be at least 55% of all mortgages issued and at least 25% of all loans issued (in terms) 2. second mortgages cannot exceed 25% of all loans issued (in terms) 3. to avoid public displeasure and the introduction of a new windfall tax the average interest rate on all loans must not exceed 15%. 4. Formulate the bank's loan problem as an LP so as to maximize interest income whilst satisfying the policy limitations. Note here that these policy conditions, whilst potentially limiting the profit that the bank can make, also limit its exposure to risk in a particular area. It is a fundamental principle of risk reduction that risk is reduced by spreading money (appropriately) across different areas.