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.

 

Answer 1

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