Question

To promote making of toilets for women, an organization tried to generate awareness through (i) house calls (ii) letters, and (iii) announcements.

The cost for each mode per attempt is given below:

(i) $Rs.50$ (ii) $Rs.20$ (iii) $Rs.40$

The number of attempts made in three village $X$, $Y$ 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 organization for three villages separately, using matrices.

Answer 1

let's find the value of cost incurred in $X,YandZ$

Cost for one house call = Rs $50$

Cost for one letter = Rs $20$

Cost for one announcement = Rs $40$

We can express the costs per contact in Rs for different types of contacting the people in matrix form as $\left[\begin{array}{ccc}50& 20& 40\end{array}\right]$

Let matrix $B$ contain the number of attempts of each type made in the three villages $X,Y\mathrm{and}Z$. The number of attempts made can be expressed in the matrix form as

$B=\left[\begin{array}{ccc}400& 300& 500\\ 300& 250& 400\\ 100& 75& 150\end{array}\right]$

We multiply $B$ and $A$.

$$\begin{gathered} BA=\left[\begin{array}{ccc}400& 300& 500\\ 300& 250& 400\\ 100& 75& 150\end{array}\right]\times \left[\begin{array}{ccc}50& 20& 40\end{array}\right] \\ =\left[\begin{array}{c}30000\\ 23000\\ 39000\end{array}\right] \end{gathered}$$

Hence, the cost incurred in village $X=Rs30,000$

Cost incurred in village $Y=Rs23000$

Cost incurred in village $Z=39000$