Formulate an LP model for this problem with the objective of maximizing the expected return (in dollars) on the portfolio. What would the formula be for the total amount spent?

A bank has $627,000 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 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, 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:

0.11X1+0.095X2+0.105X3+0.145X4