In a legislative assembly election,a political group hired a public relations firm to promote its candidate in three ways: telephone,house calls,and letters. The cost per contact (in paise) is given in matrix $A$ as $A = \begin{bmatrix} 40 \\ 100 \\ 50 \end{bmatrix} \begin{matrix} \text{Telephone} \\ \text{Housecall} \\ \text{Letter} \end{matrix}$. The number of contacts of each type made in two cities $X$ and $Y$ is given by $B = \begin{bmatrix} 1000 & 500 & 5000 \\ 3000 & 1000 & 10000 \end{bmatrix} \begin{matrix} \text{Telephone} & \text{Housecall} & \text{Letter} \\ \to X \\ \to Y \end{matrix}$. Find the total amount spent by the group in the two cities $X$ and $Y$.

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(N/A) To find the total amount spent in each city,we calculate the product $BA$.
$BA = \begin{bmatrix} 1000 & 500 & 5000 \\ 3000 & 1000 & 10000 \end{bmatrix} \begin{bmatrix} 40 \\ 100 \\ 50 \end{bmatrix}$
$= \begin{bmatrix} (1000 \times 40) + (500 \times 100) + (5000 \times 50) \\ (3000 \times 40) + (1000 \times 100) + (10000 \times 50) \end{bmatrix}$
$= \begin{bmatrix} 40000 + 50000 + 250000 \\ 120000 + 100000 + 500000 \end{bmatrix} = \begin{bmatrix} 340000 \\ 720000 \end{bmatrix}$
Thus,the total amount spent in city $X$ is $340,000$ paise (Rs. $3400$) and in city $Y$ is $720,000$ paise (Rs. $7200$).

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