Question

To promote making of toilets for women, an organisation tried to generate awarness through (i) house calls, (ii) letters, and (iii) announcements. The cost for each mode per attempt is given below:
(i) ₹50 (ii) ₹20 (iii) ₹40

The number of attempts made in three villages X, Y and Z are given below:
(i) (ii) (iii)
X 400 300 100
Y 300 250 75
Z 500 400 150

Find the total cost incurred by the organisation for three villages separately, using matrices.

Answer 1

According to the question,

Let A be the matrix showing number of attempts made in three villages X, Y and Z.
$A=\left[\begin{array}{ccc}400& 300& 100\\ 300& 250& 75\\ 500& 400& 150\end{array}\right]$

And, B be a matrix showing the cost for each mode per attempt.
$B=\left[\begin{array}{c}50\\ 20\\ 40\end{array}\right]$

Now, the total cost per village will be shown by AB.
$$\begin{gathered} AB=\left[\begin{array}{ccc}400& 300& 100\\ 300& 250& 75\\ 500& 400& 150\end{array}\right]\left[\begin{array}{c}50\\ 20\\ 40\end{array}\right] \\ =\left[\begin{array}{c}20000+6000+4000\\ 15000+5000+3000\\ 25000+8000+6000\end{array}\right] \\ =\left[\begin{array}{c}30000\\ 23000\\ 39000\end{array}\right] \end{gathered}$$

Hence, the total cost incurred by the organisation for three villages separately is
X: ₹30,000
Y: ₹23,000
Z: ₹39,000