I need help formulating a LP model to solve this question. "An investment company helps a client with 300,000 dollars to invest into 3 funds. At least 10% must be invested in a Growth and Income fund and at least 20% must be invested in a money market fund. The client has a portfolio risk index of 0.05 The risk ratings for the growth, income and money market funds are 0.10, 0.05 and 0.01 respectively. A portfolio risk index is computed as a weighted average of the risk ratings for the 3 funds where the weights are the fraction of the portfolio invested in each of the funds. The company is currently forecasting a yield of 20% on Growth fund, 10% on the income fund and 6% on the money market fund."
Oh.. forgot to add, the textbook gives the answer G = 120,000 I = 30,000 and M = 150,000
To formulate a linear programming (LP) model for this question, you need to define the decision variables, the objective function, and the constraints.
Decision Variables:
Let's assume:
- G: Amount to be invested in the Growth and Income fund,
- I: Amount to be invested in the Income fund, and
- M: Amount to be invested in the Money Market fund.
Objective Function:
The objective is to maximize the total yield or return on the investment.
Maximize: 0.20G + 0.10I + 0.06M
Constraints:
1. The total amount to be invested is $300,000:
G + I + M = 300,000
2. At least 10% of the investment must be in the Growth and Income fund:
G >= 0.1(G + I + M)
3. At least 20% of the investment must be in the Money Market fund:
M >= 0.2(G + I + M)
4. The portfolio risk index should be less than or equal to 0.05:
(0.10G + 0.05I + 0.01M)/(G + I + M) <= 0.05
5. Non-negativity constraints:
G >= 0, I >= 0, M >= 0
Now, you can solve this LP model using any appropriate optimization software or solver to find the optimal values of G, I, and M that maximize the objective function while satisfying the given constraints.