An Investor Wants to Invest $50,000 in Two Mutual Funds,A

question 4

Essay

An investor wants to invest $50,000 in two mutual funds,A and B.The rates of return,risks and minimum investment requirements for each fund are:
$\begin{array}{lrrr}&&&\text { Minimum }\\\text { Fund } & \text { Rate of return } & \text { Risk }&\text { investment }\\\hline\mathrm{A} & 12 \% & 0.5 & \$ 20,000 \\\mathrm{~B} & 9 \% & 0.3 & \$ 10.000\end{array}$
Note that a low Risk rating means a less risky investment.The investor can invest to maximize the expected rate of return or minimize risk.Any money beyond the minimum investment requirements can be invested in either fund.
The following is the multi-objective linear programming MOLP)formulation for this problem:
Let ^X₁ ^{= dollars in investment A} X₂ = dollars in investment B
MAX: ^{0.12 X}₁^{/50000 + 0.09 X}₂^/50000
MIN: ^{0.5 X}₁^{/50000 + 0.3 X}₂^/50000
Subject to: ^X₁ ^{+ X}₂ ^{= 50000}
X₁ ≥ 20000
X₂ ≥ 10000
X_i ≥ 0 for all i
The solution for the second LP is X₁,X₂)= 20,000,30,000).
Based on this solution,what values should go in cells B2:D11 of the spreadsheet?
$\begin{array}{|c|l|c|c|c|}\hline &{\text { A }} & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Problem data } & \text { A } & \text { B } & \\\hline 2 & \text { Expected return } & & & \\\hline 3 & \text { Risk rating } & & & \\\hline4 & & & & \\\hline 5 & \text { Variables } & \text { A } & \text { B } & \text { Total } \\\hline 6 & \text { Amount invested } & & & \\\hline 7 & \text { Minimum required } & & & \\\hline 8 & \\\hline 9 & \text { Objectives: } \\\hline 10 & \text { Average return } \\\hline 11 & \text { Average risk } \\\hline\end{array}$

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