| Style\Material | Steel | Wood | Glass | Paint | Concrete |
| Ranch | 5 | 20 | 16 | 7 | 17 |
| Cape \: Cod | 7 | 18 | 9 | 12 | 21 |
| Colonial | 6 | 25 | 8 | 5 | 13 |
\[C=\left( \begin{array}{ccccc} 5 & 20 & 16 & 7 & 17 \\ 7 & 18 & 9 & 12 & 21 \\ 6 & 2 & 8 & 5 & 13 \end{array} \right)\]
.Suppose we are to build 5 Ranch, 7 Cape Cod and 12 Colonial style houses respectively. We can represent this by the vector
\[\mathbf{v} = \begin{pmatrix}5\\7\\12\end{pmatrix}\]
.\[\mathbf{v}^TC =(5, 7, 12)\left( \begin{array}{ccccc} 5 & 20 & 16 & 7 & 17 \\ 7 & 18 & 9 & 12 & 21 \\ 6 & 2 & 8 & 5 & 13 \end{array} \right) = (146, 526, 260, 158, 388)\]
.\[(146, 526, 260, 158, 388) \begin{pmatrix}15\\8\\5\\1\\10\end{pmatrix}=11,736\]
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