Problem Definition.

In your finance courses, you will learn a number of techniques for creating ``optimal'' portfolios. The optimality of a portfolio depends heavily on the model used for defining risk and other aspects of financial instruments. Here is a particularly simple model that is amenable to linear programming techniques.

Consider a mortgage team with $100,000,000 to finance various investments. There are five categories of loans, each with an associated return and risk (1-10, 1 best):

Any uninvested money goes into a savings account with no risk and 3% return. The goal for the mortgage team is to allocate the money to the categories so as to:

(a) Maximize the average return per dollar

(b) Have an average risk of no more than 5 (all averages and fractions taken over the invested money (not over the saving account)).

(c) Invest at least 20% in commercial loans

(d) The amount in second mortgages and personal loans combined should be no higher than the amount in first mortgages.