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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
\[A = \begin{bmatrix}140 \\ 200 \\ 150\end{bmatrix}\begin{array}Telephone \\ House calls \\ Letters\end{array}\]
The number of contacts of each type made in two cities X and Y is given in the matrix B as
\[\begin{array}Telephone & House calls & Letters\end{array}\]
\[B = \begin{bmatrix}1000 & 500 & 5000 \\ 3000 & 1000 & 10000\end{bmatrix}\begin{array} \\City X \\ City Y\end{array}\]
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?
Solution
According to the question,
Let A be the matrix showing the cost per contact (in paisa).
\[A = \begin{bmatrix}140 \\ 200 \\ 150\end{bmatrix}\begin{array}Telephone \\ House calls \\ Letters\end{array}\]
And, B be a matrix showing the number of contacts of each type made in two cities X and Y.
\[\begin{array}Telephone & House calls & Letters\end{array}\]
\[B = \begin{bmatrix}1000 & 500 & 5000 \\ 3000 & 1000 & 10000\end{bmatrix}\begin{array}City X \\ City Y\end{array}\]
Now, the total amount spent by the party in the two cities will be shown by BA.
\[BA = \begin{bmatrix}1000 & 500 & 5000 \\ 3000 & 1000 & 10000\end{bmatrix}\begin{bmatrix}140 \\ 200 \\ 150\end{bmatrix}\]
\[ = \binom{140000 + 100000 + 750000}{420000 + 200000 + 1500000}\]
\[ = \binom{990000}{2120000}\]
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.
