The planning committee of a bank makes monthly decisions on the amount of funds to allocate to loans and to government securities. Some of the loans are secured (backed by collateral such as a home or an automobile) and some are unsecured. A list of the various types of loans and their annual rates of return are shown in the following table: Annual Rate Type of Loan of Return -------------------------------------- Secured Residential mortgage 11 Commercial mortgage 12 Automobile 15 Home improvement 13 Unsecured Vacation 17 Student 10 The current rate on government securities is 9 percent. In making its decision, the planning committee must satisfy certain legal requirements and bank policies. These can be summarized by the following set of conditions: 1. The amount allocated to secured loans must be at least four times the amount allocated to unsecured loans. 2. Auto and home loans should be no more than 20 percent of all secured loans. 3. Student loans should be no more than 30 percent of unsecured loans. 4. The amount allocated to government securities should be at least 10 percent, but no more than 20 percent, of available funds. 5. The amount allocated to vacation loans must not exceed 10 percent of all loans. The bank has $5 million dollars available for loans and investment in the next month. Formulate a linear programming model that will enable the planning committee to determine the optimal allocation of funds if the objective is to maximize the annual return, given the preceding list of conditions.