Question

In a parliament election, a political party hired a public relations firm to promote its candidates in three ways − telephone, house calls and letters. The cost per contact (in paisa) is given in matrix A as

$A=\left[\begin{array}{c}140\\ 200\\ 150\end{array}\right]\begin{array}{c}\mathrm{Telephone}\\ \mathrm{House}\mathrm{calls}\\ \mathrm{Letters}\end{array}$

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

$$\begin{gathered} \begin{array}{ccc}\mathrm{Telephone}& \mathrm{House}\mathrm{calls}& \mathrm{Letters}\end{array} \\ B=\left[\begin{array}{ccc}1000& 500& 5000\\ 3000& 1000& 10000\end{array}\right]\begin{array}{c}\mathrm{City}X\\ \mathrm{City}Y\end{array} \end{gathered}$$

Find the total amount spent by the party in the two cities.

What should one consider before casting his/her vote − party's promotional activity of their social activities?

Answer 1

According to the question,

Let A be the matrix showing the cost per contact (in paisa).
$A=\left[\begin{array}{c}140\\ 200\\ 150\end{array}\right]\begin{array}{c}\mathrm{Telephone}\\ \mathrm{House}\mathrm{calls}\\ \mathrm{Letters}\end{array}$

And, B be a matrix showing the number of contacts of each type made in two cities X and Y.
$$\begin{gathered} \begin{array}{ccc}\mathrm{Telephone}& \mathrm{House}\mathrm{calls}& \mathrm{Letters}\end{array} \\ B=\left[\begin{array}{ccc}1000& 500& 5000\\ 3000& 1000& 10000\end{array}\right]\begin{array}{c}\mathrm{City}X\\ \mathrm{City}Y\end{array} \end{gathered}$$

Now, the total amount spent by the party in the two cities will be shown by BA.
$$\begin{gathered} BA=\left[\begin{array}{ccc}1000& 500& 5000\\ 3000& 1000& 10000\end{array}\right]\left[\begin{array}{c}140\\ 200\\ 150\end{array}\right] \\ =\left[\begin{array}{c}140000+100000+750000\\ 420000+200000+1500000\end{array}\right] \\ =\left[\begin{array}{c}990000\\ 2120000\end{array}\right] \end{gathered}$$

Hence, the total amount spent by the party in the two cities is
X: ₹9900
Y: ₹21200

One should consider social activities of a party before casting his/her vote.