A bank has $614,000 in assets to allocate among investments in bonds, home mortgages, car loans, and personal loans. Bonds are expected to produce a return of 11%, mortgages 9.5%, car loans 10.5%, and personal loans 13.5%. 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, X₃, and X₄ 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, X₂, X₃, X₄ 0

(b)

Implement your model in a spreadsheet and solve it. What is the optimal solution?

(X₁, X₂, X₃, X₄) =