IV. 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: 5%

Second mortgage: 8%

Home improvement: 10%

Personal overdraft: 5%.

The bank has a maximum foreseeable lending capability of $250 million and is further constrained by the following policies:

(1) First mortgages must be at least 55 percent of all mortgages issued and at least 25 percent of all loans issued (in $ terms).

(2) Second mortgages cannot exceed 25 percent of all loans issues (in $ terms).

(3) To avoid public displeasure and a new windfall tax, the average interest rate on all loans must not exceed 7%.

Questions:

(i) Formulate the banks loan problem as a linear programming problem so as to maximize interest income while satisfying the policy limitations. (Identify the variables, objective function, and constraints.)

(ii) Use Maple (LPSolve command) to solve the linear programming problem.