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(a) Formulate an LP model for this problem with the objective of maximizing the expected return (in dollars) on the portfolio. MAX: Subject to: total amount spent amount for personal loans mortgages and personal loans bonds and personal loans X. X. X, X, 20 (b) Implement your model in a spreadsheet and solve it. What is the optimal solution?

(a) Formulate an LP model for this problem with the objective of maximizing the expected return (in dollars) on the portfolio. MAX: Subject to: total amount spent amount for personal loans mortgages and personal loans bonds and personal loans X. X. X, X, 20 (b) Implement your model in a spreadsheet and solve it. What is the optimal solution?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 89P
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A bank has $611,000 in assets to allocate among investments in bonds, home mortgages, car loans, and personal loans. Bonds are expected to produce a return of 12%, mortgages 10.5%, car loans 11.5%, and personal loans 14.5%. To make sure the portfolio is not too risky, the bank wants to restrict personal loans to no more than the 25% of the total portfolio. The bank also wants to ensure that at least as much money is invested in mortgages as is invested in personal loans. The bank also wants to invest at least as much in bonds as they do in personal loans. (Let X₁, X₂, X, and X, be the amount (in dollars) invested in bonds, mortgages, car loans, and personal loans, respectively.) (a) Formulate an LP model for this problem with the objective of maximizing the expected return (in dollars) on the portfolio. MAX: Subject to: total amount spent amount for personal loans mortgages and personal loans bonds and personal loans X₁, X. X, X ZO (b) Implement your model in a spreadsheet and solve it. What is the optimal solution? (X₂ G
Transcribed Image Text:A bank has $611,000 in assets to allocate among investments in bonds, home mortgages, car loans, and personal loans. Bonds are expected to produce a return of 12%, mortgages 10.5%, car loans 11.5%, and personal loans 14.5%. To make sure the portfolio is not too risky, the bank wants to restrict personal loans to no more than the 25% of the total portfolio. The bank also wants to ensure that at least as much money is invested in mortgages as is invested in personal loans. The bank also wants to invest at least as much in bonds as they do in personal loans. (Let X₁, X₂, X, and X, be the amount (in dollars) invested in bonds, mortgages, car loans, and personal loans, respectively.) (a) Formulate an LP model for this problem with the objective of maximizing the expected return (in dollars) on the portfolio. MAX: Subject to: total amount spent amount for personal loans mortgages and personal loans bonds and personal loans X₁, X. X, X ZO (b) Implement your model in a spreadsheet and solve it. What is the optimal solution? (X₂ G
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