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:
$\begin{array}{cccc}\text { Fund } & \text { Rate of return } & \text { Risk } & \text { Minumum investment } \\\hline \mathrm{A} & 12 \% & 0.5 & \$ 20,000 \\\mathrm{~B} & 9 \% & 0.3 & \$ 10.000\end{array}$
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 MOLP formulation for this problem:
$\begin{array} { l l } \text { Let } & \mathbf { X } _ { 1 } = \text { dollars in investment } \mathbf { A } \\& \mathbf { X } _ { \mathbf { 2 } } = \text { dollars } \text { in investment } \mathbf { B } \\\text { MAX: } & \\\text { MiN: } & 0.12 \mathbf { X } _ { 1 } / 50000 + 0.09 \mathbf { X } _ { 2 } / 50000 \\\text { Subject ta: } & 0.5 \mathbf { X } _ { 1 } / 50000 + 0.3 \mathbf { X } _ { \mathbf { 2 } } / 50000 \\& \mathbf { X } _ { 1 } + \mathbf { X } _ { \mathbf { 2 } } = 50000 \\& \mathbf { X } _ { 1 } \geq 20000 \\& \mathbf { X } _ { \mathbf { 2 } } \geq 10000 \\& \mathbf { X } _ { \mathrm { i } } \geq 0 \text { far all } i\end{array}$ The solution for the second LP is (X₁, X₂) = (20,000, 30,000).
What formulas should go in cells B2:D11 of the spreadsheet? NOTE: Formulas are not required in all of these cells.
$\begin{array}{|c|l|c|c|c|}\hline &{\text { A }} & \mathrm{B} & \mathrm{C} & \mathrm{D} \\\hline 1 & \text { Problem data } & \mathrm{A} & \mathrm{B} & \\\hline 2 & \text { Expected retum } & 12 \% & 9 \% & \\\hline 3 & \text { Risk rating } & 0.50 & 0.20 & \\\hline 4 & & & & \\\hline 5 & \text { Variables } & \mathrm{A} & \mathrm{B} & \text { Total } \\\hline 6 & \text { Amount invested } & \$ 20,000 & \$ 30,000 & \$ 50,000 \\\hline 7 & \text { Minimum required } & \$ 20,000 & \$ 10,000 & \$ 50,000 \\\hline 8 & & & & \\\hline 9 & \text { Objectives: } & & & \\\hline 10 & \text { Average return } & 10.2 \% & & \\\hline 11 & \text { Average risk } & 0.32 & & \\\hline\end{array}$

Question

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 { Minumum 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 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 } \\\text { MAX: } & \\\text { MiN: } & 0.12 \mathbf { X } _ { 1 } / 50000 + 0.09 \mathbf { X } _ { 2 } / 50000 \\\text { Subject ta: } & 0.5 \mathbf { X } _ { 1 } / 50000 + 0.3 \mathbf { X } _ { \mathbf { 2 } } / 50000 \\& \mathbf { X } _ { 1 } + \mathbf { X } _ { \mathbf { 2 } } = 50000 \\& \mathbf { X } _ { 1 } \geq 20000 \\& \mathbf { X } _ { \mathbf { 2 } } \geq 10000 \\& \mathbf { X } _ { \mathrm { i } } \geq 0 \text { far all } i\end{array}

The solution for the second LP is (X₁, X₂) = (20,000, 30,000).
What formulas should go in cells B2:D11 of the spreadsheet? NOTE: Formulas are not required in all of these cells.

\begin{array}{|c|l|c|c|c|}\hline &{\text { A }} & \mathrm{B} & \mathrm{C} & \mathrm{D} \\\hline 1 & \text { Problem data } & \mathrm{A} & \mathrm{B} & \\\hline 2 & \text { Expected retum } & 12 \% & 9 \% & \\\hline 3 & \text { Risk rating } & 0.50 & 0.20 & \\\hline 4 & & & & \\\hline 5 & \text { Variables } & \mathrm{A} & \mathrm{B} & \text { Total } \\\hline 6 & \text { Amount invested } & \$ 20,000 & \$ 30,000 & \$ 50,000 \\\hline 7 & \text { Minimum required } & \$ 20,000 & \$ 10,000 & \$ 50,000 \\\hline 8 & & & & \\\hline 9 & \text { Objectives: } & & & \\\hline 10 & \text { Average return } & 10.2 \% & & \\\hline 11 & \text { Average risk } & 0.32 & & \\\hline\end{array}

Quizplus · Accepted Answer

The Answer of 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: $\begin{array}{cccc} \text { Fund } & \text { Rate of return } & \text { Risk } & \text { Minumum investment } \ \hline \mathrm{A} & 12 \% & 0.5 & \$ 20,000 \ \mathrm{~B} & 9 \% & 0.3 & \$ 10.000 \end{array}$ 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 MOLP formulation for this problem: $$\begin{array} { l l } \text { Let } & \mathbf { X } _ { 1 } = \text { dollars in investment } \mathbf { A } \ & \mathbf { X } _ { \mathbf { 2 } } = \text { dollars } \text { in investment } \mathbf { B } \ \text { MAX: } & \ \text { MiN: } & 0.12 \mathbf { X } _ { 1 } / 50000 + 0.09 \mathbf { X } _ { 2 } / 50000 \ \text { Subject ta: } & 0.5 \mathbf { X } _ { 1 } / 50000 + 0.3 \mathbf { X } _ { \mathbf { 2 } } / 50000 \ & \mathbf { X } _ { 1 } + \mathbf { X } _ { \mathbf { 2 } } = 50000 \ & \mathbf { X } _ { 1 } \geq 20000 \ & \mathbf { X } _ { \mathbf { 2 } } \geq 10000 \ & \mathbf { X } _ { \mathrm { i } } \geq 0 \text { far all } i \end{array}$$ The solution for the second LP is (X₁, X₂) = (20,000, 30,000). What formulas should go in cells B2:D11 of the spreadsheet? NOTE: Formulas are not required in all of these cells. $\begin{array}{|c|l|c|c|c|} \hline &{\text { A }} & \mathrm{B} & \mathrm{C} & \mathrm{D} \ \hline 1 & \text { Problem data } & \mathrm{A} & \mathrm{B} & \ \hline 2 & \text { Expected retum } & 12 \% & 9 \% & \ \hline 3 & \text { Risk rating } & 0.50 & 0.20 & \ \hline 4 & & & & \ \hline 5 & \text { Variables } & \mathrm{A} & \mathrm{B} & \text { Total } \ \hline 6 & \text { Amount invested } & \$ 20,000 & \$ 30,000 & \$ 50,000 \ \hline 7 & \text { Minimum required } & \$ 20,000 & \$ 10,000 & \$ 50,000 \ \hline 8 & & & & \ \hline 9 & \text { Objectives: } & & & \ \hline 10 & \text { Average return } & 10.2 \% & & \ \hline 11 & \text { Average risk } & 0.32 & & \ \hline \end{array}$

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