M5.2 An investor wishes to invest all of her $8 million in a diversified portfolio through a commercial lender. The types of investments, the expected annual interest rate for the investment, and the maximum allowed percentage of the total portfolio that the investment can represent are shown in the table below:

INVESTMENT EXPECTED INTEREST MAXIMUM ALLOWED (% of total portfolio)

left % expected interest

right % maximum allowed (% of total portfolio)

Low-income mortgage loans 4.80% 30%

Conventional mortgage loans 4.20% 25%

Government sponsored mortgage loans 8.20% 15%

Bond investments 4.45% 40%

Stock investments 7.50% 15%

Futures trading 8.50% 10%

She wants at least 30% of her total investment in non-mortgage instruments. Furthermore, she wants no more than 20% of her total investment to be in high-yield and high-risk instruments (i.e. expected interest rate of investment is 8% or greater). Formulate and solve this problem in Excel to determine how her money should be diversified in a manner which will meet the requirements and maximize the amount of interest income. (Hint: Make sure that the LHS and RHS of constraints are the same units) SOLUTION: The optimal solution, the value of the interest income, should be $463,400 ( $10 for rounding). The minimum invested in any one investment is $0. The maximum invested in any one investment is $2,800,000.

Written out constraints with solver