In a legislative assembly election,

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

The number of contacts of each type made in two cities $X$ and $Y$ is given in matrix $B$ as

Find the total amount spent by the group in the two cities X and Y.

Solution:

The cost per contact in paise">(in paise)in paise is given by

$A=\left[\begin{array}{c}40 \\ 100 \\ 50\end{array}\right] \begin{gathered}\text { Telephone } \\ \text { Housecall } \\ \text { Letter }\end{gathered}$

The number of contacts of each type made in the two cities X and Y is given by

B=\left[\begin{array}{ccr}\text { Telephone } & \text { Housecall } & \text { Letter } \\ 1000 & 500 & 5000 \\ 3000 & 1000 & 10000\end{array}\right] \quad \begin{aligned}&X \\&Y\end{aligned}

Total amount spent by the group in the two cities X and Y is given by

$B A=\left[\begin{array}{ccc}1000 & 500 & 5000 \\ 3000 & 1000 & 10000\end{array}\right]\left[\begin{array}{c}40 \\ 100 \\ 50\end{array}\right]$

$=\left[\begin{array}{c}40000+50000+250000 \\ 120000+100000+500000\end{array}\right]$

=\left[\begin{array}{l}340000 \\ 720000\end{array}\right] \begin{aligned}&X \\&Y\end{aligned}

Thus,

Amount spent on $X=$ Rs 3400

Amount spent on $Y=$ Rs 7200