A trust officer at the Blacksburg National Bank needs to determine how to invest $100,000 in the following collection of bonds to maximize the total annual return (before tax). Bond Annual Return Maturity Risk Tax-Free A 9.5% Long High Yes B 8.0% Short Low Yes C 9.0% Long Low No D 9.0% Long High Yes E 9.0% Short High No The officer wants to invest as least 50% of the money in short-term issues and no more than 50% in high-risk issues. At least 30% of the funds should go in tax-free investments, and at least 40% of the total annual return should be tax free. Suppose the decision variable represents the amount of money invested in bond for . Formulate a linear programming (LP) model to solve the optimal strategy. 1. Write down the constraint using the defined decision variables requiring “invest as least 50% of the money in short-term issues”. 2. Write down the constraint using the defined decision variables requiring “at least 30% of the funds should go in tax-free investments”.
A trust officer at the Blacksburg National Bank needs to determine how to invest $100,000 in the following collection of bonds to maximize the total annual return (before tax).
|
Bond |
Annual Return |
Maturity |
Risk |
Tax-Free |
|
A |
9.5% |
Long |
High |
Yes |
|
B |
8.0% |
Short |
Low |
Yes |
|
C |
9.0% |
Long |
Low |
No |
|
D |
9.0% |
Long |
High |
Yes |
|
E |
9.0% |
Short |
High |
No |
The officer wants to invest as least 50% of the money in short-term issues and no more than 50% in high-risk issues. At least 30% of the funds should go in tax-free investments, and at least 40% of the total annual return should be tax free.
Suppose the decision variable represents the amount of money invested in bond for . Formulate a linear programming (LP) model to solve the optimal strategy.
1. Write down the constraint using the defined decision variables requiring “invest as least 50% of the money in short-term issues”.
2. Write down the constraint using the defined decision variables requiring “at least 30% of the funds should go in tax-free investments”.
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