Mr. Lothbrok Has $10,000 To Invest In Two Mutual Funds

Question

Mr Lothbrok Has 10000 To Invest In Two Types Of Mutual Funds Colem Mr. Lothbrok has $10,000 to invest in two types of mutual funds: the Coleman High-Yield Fund, which offers an annual yield of 6%, and the Coleman Equity Fund, which earns 10%. He intends to invest at least $5,000 in the High-Yield Fund and at least $2,000 in the Equity Fund. The goal is to determine how much money he should allocate to each fund to maximize his total annual yield, and to identify the maximum yield achievable under these constraints.

Dr. Jack HW Helper · Accepted Answer

Optimizing investment strategies to maximize returns within given constraints is a fundamental problem in financial mathematics, often approached through linear programming techniques. In this scenario, Mr. Lothbrok's objective is to allocate his $10,000 investment between two mutual funds to maximize annual yield while respecting minimum investment constraints. Problem Restatement The variables are: Let $ x $ be the amount invested in the High-Yield Fund, with the constraint $ x \geq 5000 $. Let $ y $ be the amount invested in the Equity Fund, with the constraint $ y \geq 2000 $. The total investment constraint is: $ x + y \leq 10,000 $. The objective function, representing total annual yield, is: Maximize $ Z = 0.06x + 0.10y $. Solution Approach This is a linear programming problem with constraints. The feasible region is bounded by the constraints: $ x \ge 5000 $, $ y \ge 2000 $, and $ x + y \le 10,000 $. Optimal solutions in linear programming lie at corner points of the feasible region. Therefore, identify the vertices of this feasible region and evaluate the objective function at each. Identifying Corner Points - Constraint lines: - $ x = 5000 $ (minimum investment in High-Yield fund) - $ y = 2000 $ (minimum investment in Equity fund) - $ x + y = 10,000 $ (total investment limit) - Corner points: 1. Intersection of $ x = 5000 $ and $ y = 2000 $: - $ x=5000 $, $ y=2000 $, - Total: $ 5000 + 2000 = 7000 $, less than 10,000, feasible. 2. Intersection of $ x=5000 $ and $ x + y=10,000 $: - $ x=5000 $, $ y=10,000 - 5000=5000 $, - Feasible and satisfies $ y \ge 2000 $. 3. Intersection of $ y=2000 $ and $ x + y=10,000 $: - $ y=2000 $, $ x=10,000 - 2000=8,000 $, - Feasible and satisfies $ x \ge 5000 $. - Check these corner points: 1. $ (x=5000, y=2000) $ 2. $ (x=5000, y=5000) $ 3. $ (x=8000, y=2000) $ Note that the remaining point is where $ x + y=10,000 $ intersects the boundary conditions. Calculating the O

Mr. Lothbrok Has $10,000 To Invest In Two Mutual Funds

Mr Lothbrok Has 10000 To Invest In Two Types Of Mutual Funds Colem

Paper For Above instruction

Problem Restatement

Solution Approach

Identifying Corner Points

Calculating the Objective Function at Each Point

Conclusion

Final Investment Plan and Yield

References