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
$A=\begin{array}{c}\mathrm{Cost}\mathrm{per}\mathrm{contact}\\ \begin{array}{c}\left[\begin{array}{c}40\\ 100\\ 50\end{array}\right]\end{array}\end{array}\begin{array}{c}\\ \begin{array}{c}\mathrm{Telephone}\\ \mathrm{House}\mathrm{call}\\ \mathrm{Letter}\end{array}\end{array}$
The number of contacts of each type made in two cities X and Y is given in matrix B as
$\begin{array}{c}\begin{array}{ccc}\mathrm{Telephone}& \mathrm{House}\mathrm{call}& \mathrm{Letter}\end{array}\\ B=\left[\begin{array}{ccc}1000& 500& 5000\\ 3000& 1000& 10000\end{array}\right]\end{array}\begin{array}{c}\\ \to X\\ \to Y\end{array}$
Find the total amount spent by the group in the two cities X and Y.

Answer 1

The cost per contact $\left(inpaise\right)$ is given by

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

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

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

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

$$\begin{gathered} BA=\left[\begin{array}{ccc}1000& 500& 5000\\ 3000& 1000& 10000\end{array}\right]\left[\begin{array}{c}40\\ 100\\ 50\end{array}\right] \\ =\left[\begin{array}{c}40000+50000+250000\\ 120000+100000+500000\end{array}\right] \\ =\left[\begin{array}{c}340000\\ 720000\end{array}\right]\begin{array}{c}X\\ Y\end{array} \end{gathered}$$

Thus,
Amount spent on X = Rs 3400
Amount spent on Y = Rs 7200