Question

George Johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a stock fund. The projected returns over the life of the investments are 9% for the bond fund and 11% for the stock fund. Whatever portion of the inheritance he finally decides to commit to the trust fund, he wants to invest at least 40% of that amount in the bond fund. In addition, he wants to select a mix that will enable him to obtain a total return of at least 9.5%. Let B = percentage of funds invested in the bond fund S = percentage of funds invested in the stock fund Max or Min ___B + ___S s.t. ___ B =, or = ____ Bond fund minimum ___ B + ___ S =, or = ____ Minimum return ___ B + ___ S =, or = ____ Percentage requirement Solve the problem. If required, round the answers to one decimal place. Optimal solution: B = S = Value of optimal solution is ____%

A. Max, 0.6B + 0.4S, B≥0,S≥0, 0.4B + 0.6S ≥ 0.095(B + S), B + S = 1, Optimal solution: B = 0.4, S = 0.6, Value of optimal solution is 10.0%

B. Max, 0.4B + 0.6S, B≥0,S≥0, 0.6B + 0.4S ≥ 0.095(B + S), B + S = 1, Optimal solution: B = 0.6, S = 0.4, Value of optimal solution is 9.0%

C. Min, 0.6B + 0.4S, B≥0,S≥0, 0.4B + 0.6S ≥ 0.095(B + S), B + S = 1, Optimal solution: B = 0.4, S = 0.6, Value of optimal solution is 9.5%

D. Min, 0.4B + 0.6S, B≥0,S≥0, 0.6B + 0.4S ≥ 0.095(B + S), B + S = 1, Optimal solution: B = 0.6, S = 0.4, Value of optimal solution is 10.5%

Answer 1

To solve this problem, we need to set up a linear programming model with constraints and an objective function. The optimal solution is B = 0.4 and S = 0.6, with a value of 10.0%.

Step-by-step explanation:

To solve this problem, we need to set up a linear programming model. Let B represent the percentage of funds invested in the bond fund and S represent the percentage of funds invested in the stock fund. The objective function is to maximize the total return, so the equation is B + S. We also have the following constraints:

• B ≥ 0.4 (he wants to invest at least 40% in the bond fund)
• B + S = 1 (the total percentage of funds invested must be 100%)
• 0.4B + 0.6S ≥ 0.095(B + S) (the minimum return requirement is 9.5%, so we need to ensure the weighted average return is at least 9.5%)

After solving the linear programming model, the optimal solution is B = 0.4 and S = 0.6. The value of the optimal solution is 10.0%. Therefore, option A is the correct answer.