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Question
In a legislative assembly election, a political group hired a public relations firm to promote its candidates in three ways: telephone, house calls and letters. The cost per contact (in paise) is given matrix A as
Cost per contact
`A=[[40],[100],[50]]` `[["Teliphone"] ,["House call "],[" letter"]]`
The number of contacts of each type made in two cities X and Y is given in matrix B as
Telephone House call Letter
`B= [[ 1000, 500, 5000],[3000,1000, 10000 ]]`
Find the total amount spent by the group in the two cities X and Y.
Solution
The cost per contact
\[\left( in paise \right)\] is given by
\[A = \begin{bmatrix}40 \\ 100 \\ 50\end{bmatrix}\begin{array}"Telephone \\ Housecall \\ Letter\end{array}\]
The number of contacts of each type made in the two cities X and Y is given by
Telephone Housecall Letter
\[B = \begin{bmatrix}1000 & 500 & 5000 \\ 3000 & 1000 & 10000\end{bmatrix} \begin{array}"X \\ Y\end{array}\]
Total amount spent by the group in the two cities X and Y is given by
\[BA = \begin{bmatrix}1000 & 500 & 5000 \\ 3000 & 1000 & 10000\end{bmatrix}\begin{bmatrix}40 \\ 100 \\ 50\end{bmatrix}\]
`=[[ 40000 + 50000 + 250000],[120000 + 100000 + 500000]]`
`=[[340000],[720000]]` \[\begin{matrix}X\\Y\end{matrix}\]
Thus,
Amount spent on X = Rs 3400
Amount spent on Y = Rs 7200
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