## Maximising Revenue With Matrices

\[\begin{pmatrix}900\\700\\400\end{pmatrix}\]

.The table shows the price of a box of each type of fruit in nations of the UK..

Nation\Fruit | Orange | Grapefruit | Tangerine |

England | 4 | 2 | 3 |

Northern Ireland | 5 | 1 | 2 |

Scotland | 4 | 3 | 2 |

Wales | 3 | 2 | 5 |

\[\left( \begin{array}{cccc} 4 & 2 & 3 \\ 5 & 1 & 2 \\ 4 & 3 & 2 \\ 3 & 2 & 5 \end{array} \right)\]

.We can find a vector representing the total revenue from selling all the produce in each country by multiplying the above matrix by the above vector.

\[\left( \begin{array}{cccc} 4 & 2 & 3 \\ 5 & 1 & 2 \\ 4 & 3 & 2 \\ 3 & 2 & 5 \end{array} \right) \begin{pmatrix}900\\700\\400\end{pmatrix}=\begin{pmatrix}4 \times 900+2 \times 700 +3 \times 400\\5 \times 900+1 \times 700+_2 \times 400\\4 \times 900 + 3 \times 700 + 2 \times 400 \\ 3 \times 900 + 2 \times 700 + 5 \times 400 \end{pmatrix}= \begin{pmatrix}6200\\6000\\6500\\6100\end{pmatrix}\]

.The fruit grower show sell his fruit in Scotland.