Problem 4 Consider a mortgage team with S1000K to finance various investments. T

Question

Problem 4 Consider a mortgage team with S1000K to finance various investments. There are five cate- gories of loans, each with an associated return and risk (1-10, 1 is the best) as follows Return(%) Risk Loan/investment First Mortgages Second Mortgages Personal Loans Commercial Loans Government Securities 12 15 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 (i) Maximize the total return (ii) Have an average risk of no more than 5. The average is taken over the invested money, not over the saving account (iii) Invest at least 20% in commercial loans (of the total amount invested). (iv) The amount in second mortgages and personal loans combined should be no higher than the amount in first mortgages Formulate the problem as an LP and solve it in Excel. Clearly indicate your decision variables, your objective function, and your constraints. Attach the Answer Report to your HW.

Explanation / Answer

Solution:

Let Xi denote the amount of money invested in option "i".
Maximize Total Return per dollar = Z = 9X1+ 12X2+ 15X3+8X4 + 6X5
Subject to:
(1) The total amount of money available for investment is $100,000,000;
X1+X2+X3+X4+X5 100,000,000
Note that we cannot use "=" in this constraint as it states that the any uninvested money goes into savings account with no risk and 3% return.
(2) Have an average risk of no more than 5 (all averages and fractions taken over the invested money (not over the saving account)).
9X1+ 12X2 + 15X3 + 8X4+ 6X5
5
X1+ X2+ X3+ X4+ X5
or 9X1+ 12X2+ 15X3+ 8X4+ 6X5 5(X1+ X2+ X3+X4+X5
(3) Invest at least 20% in commercial loans
X4 0.20 *100,000,000
(4) The amount in second mortgages and personal loans combined should be no higher than the amount in first mortgages.
X2+ X3 X1
(5) All variables are non-negative.
X1, X2, X3, X4,X5 0

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