A bank is attempting to determine where its assets should be invested during the current year. At present, $1,000,000 is available for investment in bonds, home loans, auto loans, and personal loans. The annual rate of returns are shown in the table below.

INVESTMENT ANNUAL RATE OF RETURN

Bonds 10%

Mortgage 16%

Home Equity 14%

Auto Loans 12%

Personal Loans 17%

The banker wants to maximize the amount of interest income generated for the bank. To ensure that the banks portfolio is not too risky, the banks investment manager has placed the following three restrictions on the banks portfolio:

The amount invested in auto loans must be at least 10% of the total amount invested.

No more than 25% of the total amount invested can be in mortgage loans.

The amount invested in personal loans cannot exceed the annual amount invested in bonds.

The amount invested in mortgage and home equity loans cannot exceed 40% of the total amount invested

No more than 15% of the total amount invested can be in personal loans.

SOLUTION: The optimal solution, the value of the interest income, should be $137,500 ( $10 for rounding).

Formulation: Formulate this problem by defining decision variables, objective function, and constraints in standard format as specified/demonstrated in videos.