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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 is shown in the following table: Type of Loan Annual Rate of Return (%) Secured Residential mortgage 11 Commercial mortgage 12 Motorcar 14 Home improvement 13 Unsecured Vacation 16 Student 9. The current rate on government securities is 9%.

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 is shown in the following table: Type of Loan Annual Rate of Return (%) Secured Residential mortgage 11 Commercial mortgage 12 Motorcar 14 Home improvement 13 Unsecured Vacation 16 Student 9. The current rate on government securities is 9%.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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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 is shown in the following table: Type of Loan Annual Rate of Return (%) Secured 11 Residential mortgage Commercial mortgage 12 Motorcar 14 Home improvement 13 Unsecured Vacation 16 Student 9. The current rate on government securities is 9%.
Transcribed Image Text: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 is shown in the following table: Type of Loan Annual Rate of Return (%) Secured 11 Residential mortgage Commercial mortgage 12 Motorcar 14 Home improvement 13 Unsecured Vacation 16 Student 9. The current rate on government securities is 9%.
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. 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 government 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 conditions.
Transcribed Image Text: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. 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 government 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 conditions.
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