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 retur is shown in the following table: Annual Rate of Return (%) Type of Loan Secured Residential mortgage Commercial mortgage Motorcar Home improvement 11 12 13 Unsecured Vacation Student 16 9 The current rate on goverment securities is 9% TURN OVER In making its decision, the planning committee must satisty certain legal requirements and barik policies These can be summarized by the following set of conditions The amount allocated to secured loans must be at least four times the amount allocated to unsecured loans The total value of car and home loans should be no more than 20% of the value of all secured loans. The value of student loans should be no more than 30% of unsecured loans. The amount allocated to goverment securities should be at least 10%, but no more than 20% of available funds. The amount allocated to vacation loans must not exceed 10% of all loans. The bank has $5 million available for loans and investments 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 of conditions