A client who contacted CWD this past week has a maximum of $50,000 to invest. CWD's has two investment funds. The projected return for internet fund is 12% and Blue chip 9%. The investment advisior requires that at most $35,000 of the client's funds should be invested in the internet fund. Risk rate internet fund 6 per 1000 and Blue chip 4 per 1000. CWD recommends that a client who is a moderate investor limit his portfolio to a maximum risk of 240. Formulate a linear programming model that can be used to determine the recommended investment portfolio to maximize annual return.
To formulate a linear programming model for this problem, we need to define the decision variables, objective function, and constraints.
Decision Variables:
Let x be the amount invested in the internet fund (in thousands of dollars).
Let y be the amount invested in the blue chip fund (in thousands of dollars).
Objective Function:
Maximize the annual return. The annual return can be calculated as the sum of the returns from the internet fund and the blue chip fund.
Objective Function: Maximize 0.12x + 0.09y (the annual return in thousands of dollars).
Constraints:
1. The total investment should not exceed the client's maximum investment amount of $50,000:
x + y ≤ 50
2. The investment in the internet fund should be at most $35,000:
x ≤ 35
3. The risk level of the investment portfolio should be limited to a maximum of 240:
(6/1000)x + (4/1000)y ≤ 240
4. Non-negativity constraints:
x ≥ 0
y ≥ 0
Therefore, the linear programming model can be written as follows:
Maximize: 0.12x + 0.09y
Subject to:
x + y ≤ 50
x ≤ 35
(6/1000)x + (4/1000)y ≤ 240
x ≥ 0
y ≥ 0
Solving this linear program will provide the recommended investment portfolio that maximizes the annual return, while considering the investment limits and risk requirement.