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

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:
$\begin{array}{cccc}\text { Fund } & \text { Rate of return } & \text { Risk } & \text { Minimum investment } \\\hline \mathrm{A} & 12 \% & .5 & \$ 20,000 \\\mathrm{~B} & 9 \% & 3 & \$ 10.000\end{array}$
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 MOLP formulation for this problem:
$\begin{array} { l l } \text { Let } & \mathbf { X } _ { 1 } = \text { dollars in investment } \mathbf { A } \\& \mathbf { X } _ { \mathbf { 2 } } = \text { dollars } \text { in investment } \mathbf { B } \\\end{array}$

$\begin{array}{ll}\text { MAX: } & 0.12 \mathrm{X}_{1} / 50000+0.09 \mathrm{X}_{2} / 50000 \\\text { MIN: } & 0.5 \mathrm{X}_{1} / 50000+0.3 \mathrm{X}_{2} / 50000 \\\text { Subject to: } & \mathrm{X}_{1}+\mathrm{X}_{2}=500000 \\& \mathrm{X}_{1} \geq 20000 \\& \mathrm{X}_{2} \geq 10000 \\& \mathrm{X}_{\mathrm{i}} \geq 0 \text { for all } \mathrm{i}\end{array}$

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?
$\begin{array}{|c|l|c|c|c|}\hline & {\text { A }} & \text { B } & \text { C } & \text { D } \\\hline 1 & \text { Problem data } & \text { A } & \text { B } & \\\hline 2 & \text { Expected retum } & & & \\\hline 3 & \text { Risk rating } & & & \\\hline 4 & & & & \\\hline 5 & \text { Variables } & \text { A } & \text { B } & \text { Total } \\\hline 6 & \text { Amount invested } & & & \\\hline 7 & \text { Minimum required } & & & \\\hline 8 & & & & \\\hline 9 & \text { Objectives: } & & & \\\hline 10 & \text { Average return } & & & \\\hline 11 & \text { Average risk } & & & \\\hline\end{array}$