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:
first mortgages must be at least 55% of all mortgages issued and at least 25% of all loans issued (in £ terms)
second mortgages cannot exceed 25% of all loans issued (in £ terms)
to avoid public displeasure and the introduction of a new windfall tax the average interest rate on all loans must not exceed 15%.
Formulate the bank's loan problem as an LP so as to maximize interest income whilst satisfying the policy limitations.
