A bank's planning committee makes monthly decisions about the amount of funds to allocate for government loans
Question:
A bank's planning committee makes monthly decisions about the amount of funds to allocate for government loans and securities. Some of the loans are secured (backed by collateral like a house or car) and some are unsecured. A list of the different types of loans and their annual rates of return as shown below:
investment type | annual rate of return |
Secured Loans: | |
Residential Mortgage (x 1 ) | 11 |
Commercial Mortgage (x 2 ) | 12 |
Car ( x3 ) | 15 |
Home Improvement (x 4 ) | 13 |
Unsecured loans: | |
Holidays ( x5 ) | 17 |
Student ( x6 ) | 10 |
Government bonds (x 7 ) | 9 |
The bank has £5 million available for lending and investment in the next month. In making its decision, the planning committee must comply with certain legal requirements and bank policies. These can be summarized in 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) Car and home loans should not be more than 20% of all secured loans.
3) Student loans should not be more than 30% of unsecured loans.
4) The amount allocated to government securities must be at least 10%, but not more than 20%, of the available funds
5) The amount allocated to vacation loans must not exceed 10% of the total loans.
Required:
Formulate a linear programming model that allows the planning committee to determine the optimal allocation of funds if the objective is to maximize the annual, given the above list of conditions.
Formulate this problem as an LP problem.
Quantitative Methods for Business
ISBN: 978-0324651751
11th Edition
Authors: David Anderson, Dennis Sweeney, Thomas Williams, Jeffrey cam