An Investor Has $500,000 to Invest and Wants to Maximize

Essay

An investor has $500,000 to invest and wants to maximize the money they will receive at the end of one year. They can invest in condos, apartments and houses. The profit after one year, the cost and the number of units available are shown below.
$\begin{array}{clccc}&& \text { Profit } & \text { Cost } & \text { Number}\\\text { Variable } & \text { Investment } & (\$ 1,000) & (\$ 1,000) & \text { Available } \\\hline \mathrm{X}_{1} & \text { Condos } & 6 & 50 & 10 \\\mathrm{X}_{2} & \text { Apartments } & 12 & 90 & 5 \\\mathrm{X}_{3} & \text { Houses } & 9 & 100 & 7\end{array}$
Based on this ILP formulation of the problem and the indicated optimal integer solution values what values should go in cells B5:F12 of the following Excel spreadsheet?
MAX: $\quad 6 \mathbf { X } _ { 1 } + 12 \mathbf { X } _ { \mathbf { 2 } } + 9 \mathbf { X } _ { \mathbf { 3 } }$
Subject to:
$\begin{array} { l } 50 X _ { 1 } + 90 X _ { \mathbf { 2 } } + 100 X _ { \mathbf { 3 } } \leq 500 \\\mathbf { X } _ { 1 } \leq 10 \\\mathbf { X } _ { \mathbf { 2 } } \leq 5 \\\mathbf { X } _ { \mathbf { 3 } } \leq 7 \\\mathbf { X } _ { \mathrm { i } } \geq 0 \text { and integer }\end{array}$
Salution: $\left( \mathbf { X } _ { 1 } , \mathbf { X } _ { 2 } \mathbf { X } _ { \mathbf { 3} } \right) = ( 1,5, 0)$