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The Versatile Lender Inc (VLI) is planning the allocation of new funds for the coming year. They make five types of loans: personal loans, student loans, home equity loans, machinery/equipment loans, and loans against fixed deposits. The annual return rate on these loans is 7% on personal loans, 2.5% on student loans, 4.25% on home equity loans, 10.75% on machinery/equipment loans, and 6% on loans against fixed deposits. The VLI's planning committee has decided following conditions must be met. • At least 45% of the amount of new funds disbursed must be allocated to home equity loans. The amount allocated to student loans must be 15% of the amount of new funds disbursed. Loan against fixed deposit should be at least 25% of the sum of loans allocated to personal loans, home equity loans and machinery loans. Personal loans should not exceed 1.5 times the loan allocated to student loans. The amount allocated to machinery/equipment loans must be at most 30% of the home equity loans. • Variables are defined as follows: P = amount allocated to personal loans S = amount allocated to student loans (a) (b) H = amount allocated to home equity loans M = amount allocated to machinery/equipment loans F = amount allocated to loans against fixed deposits Must use the above defined variables to formulate a linear programming model that can determine the amount of funds VLI should allocate to each type of loan to maximize the total annual return for the new funds. Formulate the objective function. Specify/state all the constraint/s such that only constants appear on the right-hand sides of constraint/s.

The Versatile Lender Inc (VLI) is planning the allocation of new funds for the coming year. They make five types of loans: personal loans, student loans, home equity loans, machinery/equipment loans, and loans against fixed deposits. The annual return rate on these loans is 7% on personal loans, 2.5% on student loans, 4.25% on home equity loans, 10.75% on machinery/equipment loans, and 6% on loans against fixed deposits. The VLI's planning committee has decided following conditions must be met. • At least 45% of the amount of new funds disbursed must be allocated to home equity loans. The amount allocated to student loans must be 15% of the amount of new funds disbursed. Loan against fixed deposit should be at least 25% of the sum of loans allocated to personal loans, home equity loans and machinery loans. Personal loans should not exceed 1.5 times the loan allocated to student loans. The amount allocated to machinery/equipment loans must be at most 30% of the home equity loans. • Variables are defined as follows: P = amount allocated to personal loans S = amount allocated to student loans (a) (b) H = amount allocated to home equity loans M = amount allocated to machinery/equipment loans F = amount allocated to loans against fixed deposits Must use the above defined variables to formulate a linear programming model that can determine the amount of funds VLI should allocate to each type of loan to maximize the total annual return for the new funds. Formulate the objective function. Specify/state all the constraint/s such that only constants appear on the right-hand sides of constraint/s.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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The Versatile Lender Inc (VLI) is planning the allocation of new funds for the coming year. They make five types of loans: personal loans, student loans, home equity loans, machinery/equipment loans, and loans against fixed deposits. The annual return rate on these loans is 7% on personal loans, 2.5% on student loans, 4.25% on home equity loans, 10.75% on machinery/equipment loans, and 6% on loans against fixed deposits. The VLI's planning committee has decided following conditions must be met. At least 45% of the amount of new funds disbursed must be allocated to home equity loans. The amount allocated to student loans must be 15% of the amount of new funds disbursed. Loan against fixed deposit should be at least 25% of the sum of loans allocated to personal loans, home equity loans and machinery loans. Personal loans should not exceed 1.5 times the loan allocated to student loans. The amount allocated to machinery/equipment loans must be at most 30% of the home equity loans. • Variables are defined as follows: P = amount allocated to personal loans S = amount allocated to student loans (a) (b) H = amount allocated to home equity loans M = amount allocated to machinery/equipment loans F = amount allocated to loans against fixed deposits Must use the above defined variables to formulate a linear programming model that can determine the amount of funds VLI should allocate to each type of loan to maximize the total annual return for the new funds. Formulate the objective function. Specify/state all the constraint/s such that only constants appear on the right-hand sides of constraint/s.
Transcribed Image Text:The Versatile Lender Inc (VLI) is planning the allocation of new funds for the coming year. They make five types of loans: personal loans, student loans, home equity loans, machinery/equipment loans, and loans against fixed deposits. The annual return rate on these loans is 7% on personal loans, 2.5% on student loans, 4.25% on home equity loans, 10.75% on machinery/equipment loans, and 6% on loans against fixed deposits. The VLI's planning committee has decided following conditions must be met. At least 45% of the amount of new funds disbursed must be allocated to home equity loans. The amount allocated to student loans must be 15% of the amount of new funds disbursed. Loan against fixed deposit should be at least 25% of the sum of loans allocated to personal loans, home equity loans and machinery loans. Personal loans should not exceed 1.5 times the loan allocated to student loans. The amount allocated to machinery/equipment loans must be at most 30% of the home equity loans. • Variables are defined as follows: P = amount allocated to personal loans S = amount allocated to student loans (a) (b) H = amount allocated to home equity loans M = amount allocated to machinery/equipment loans F = amount allocated to loans against fixed deposits Must use the above defined variables to formulate a linear programming model that can determine the amount of funds VLI should allocate to each type of loan to maximize the total annual return for the new funds. Formulate the objective function. Specify/state all the constraint/s such that only constants appear on the right-hand sides of constraint/s.
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