A Financial Planner Wants to Design a Portfolio of Investments

Essay

A financial planner wants to design a portfolio of investments for a client. The client has $400,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 30% of the money in any one investment, at least one half should be invested in long-term bonds which mature in six or more years, and no more than 40% of the total money should be invested in B or C since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio.
$$\begin{array} { c c c l } \text { Investment } & \text { Return } & \text { Years to Maturity } & \text { Rating } \\\hline \mathbf { A } & 6.45 \% & 6 & \text { 1-Excellent } \\\text { B } & 8.5 \% & 5 & \text { 3-Gaod } \\\text { C } & 9.00 \% & 8 & \text { 4-Fair } \\\text { D } & 7.75 \% & 4 & \text { 2-Very Gaod }\end{array}$$ $$\begin{array} { l l } \text { Let } & \mathbf { X } _ { 1 } = \text { Dollars invested in } \mathrm { A } \\& \mathbf { X } _ { \mathbf { 2 } } = \text { Dollars invested in } \mathrm { B } \\& \mathbf { X } _ { \mathbf { 3 } } = \text { Dollars invested in } \mathrm { C } \\& \mathbf { X } _ { 4 } = \text { Dollars invested in } \mathrm { D } \\& \\ \text { MAX: } & \mathbf { X } 45 \mathbf { X } _ { 1 } + .085 \mathbf { X } _ { \mathbf { 2 } } + \text {. } 990 \mathbf { X } _ { \mathbf { 3 } } + .075 \mathbf { X } _ { 4 } \\\text { Subject to: } & \mathbf { X } _ { 1 } + \mathbf { X } _ { \mathbf { 2 } } + \mathbf { X } _ { \mathbf { 3 } } + \mathbf { X } _ { 4 } \leq 400000 \\& \mathbf { X } _ { 1 } \leq 120000 \\& \mathbf { X } _ { \mathbf { 2 } } \leq 120000 \\& \mathbf { X } _ { 3 } \leq 120000 \\& \mathbf { X } _ { 4 } \leq 120000 \\& \mathbf { X } _ { 1 } + \mathbf { X } _ { 3 } \geq 200000 \\& \mathbf { X } _ { \mathbf { 2 } } + \mathbf { X } _ { 3 } \leq 160000 \\& \mathbf { X } _ { 1 } \mathbf { X } _ { \mathbf { 2 } } \mathbf { X } _ { \mathbf { 3 } } \mathbf { X } _ { 4 } \geq 0\end{array}$$ What formulas are required for the following cells in the Excel spreadsheet implementation of the formulation?
B7
D7
F7
H7