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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
$A = \left[ {\begin{array}{*{20}{c}}
{\mathrm {Cost\,\,per\,\,contact}} \\
{40} \\
{100} \\
{50}
\end{array}} \right]\begin{array}{*{20}{l}}
{{\text{ Telephone }}} \\
{{\text{ Housecall }}} \\
{{\text{ Letter }}}
\end{array}$
The number of contacts of each type made in two cities $\mathrm{X}$ and $\mathrm{Y}$ is given by
$B=$$\,\left[ {\begin{array}{*{20}{c}}
{\mathrm {Telephone}}&{\mathrm {Housecall}}&{\mathrm {Letter}} \\
{1000}&{500}&{5000} \\
{3000}&{1000}&{10,000}
\end{array}} \right]\,$ $\begin{array}{*{20}{c}}
{} \\
{ \to X} \\
{ \to \,Y}
\end{array}$. Find the total amount spent by the group in the two cities $\mathrm{X}$ and $\mathrm{Y}$.
Solution
We have
$BA=$ ${\mkern 1mu} \left[ {\begin{array}{*{20}{c}}
{40,000}&{50,000}&{250,000} \\
{120,000}&{100,000}&{500,000}
\end{array}} \right]{\mkern 1mu} $ $\begin{array}{*{20}{c}}
{ \to X} \\
{ \to \,Y}
\end{array}$
$ = \,{\mkern 1mu} \left[ {\begin{array}{*{20}{c}}
{340,000} \\
{720,000}
\end{array}} \right]{\mkern 1mu} \begin{array}{*{20}{c}}
{\, \to \,X} \\
{ \to \,Y}
\end{array}$
So the total amount spent by the group in the two cities is $340,000$ paise and $720,000$ paise, i.e., Rs. $3400$ and Rs. $7200,$ respectively.