A person is looking to invest $100,000 in hopes of getting the highest return possible. There are 4 investment options available: bonds, mutual funds, stocks, or a saving account yielding interest. The bonds give a 3% annual return, mutual funds give an 8% return, stocks give a 10% return, and the savings account gives a 2% return (all investments subject to risk). To control for risk, several constraints are put into place: 1. No more than 15% of the total investment can be put into stocks. 2. At least 40% must be invested in mutual funds and/or the savings account. 3. The amount put in the savings account must be no more than the amount put into the other investments combined. 4. The ratio of money invested in bonds and mutual fund to the amount in stocks and the savings account should be at least 1.2 to 1. 5. All $100,000 must be invested and no shorting is allowed (It means there will be no “borrowed” money”) Formulate a linear programming model for this problem to get the highest return. (You just need to define all the variables X1, X2, X3…, then state the Objective Function and all the constraints)
A person is looking to invest $100,000 in hopes of getting the highest return possible. There are 4 investment options available: bonds, mutual funds, stocks, or a saving account yielding interest. The bonds give a 3% annual return, mutual funds give an 8% return, stocks give a 10% return, and the savings account gives a 2% return (all investments subject to risk). To control for risk, several constraints are put into place:
1. No more than 15% of the total investment can be put into stocks.
2. At least 40% must be invested in mutual funds and/or the savings account.
3. The amount put in the savings account must be no more than the amount put into the other investments combined.
4. The ratio of money invested in bonds and mutual fund to the amount in stocks and the savings account should be at least 1.2 to 1.
5. All $100,000 must be invested and no shorting is allowed (It means there will be no “borrowed” money”)
Formulate a linear
Step by step
Solved in 3 steps
