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.

\[A = \begin{bmatrix}400 & 300 & 100 \\ 300 & 250 & 75 \\ 500 & 400 & 150\end{bmatrix}\]

And, B be a matrix showing the cost for each mode per attempt.

\[B = \begin{bmatrix}50 \\ 20 \\ 40\end{bmatrix}\]

\[AB = \begin{bmatrix}400 & 300 & 100 \\ 300 & 250 & 75 \\ 500 & 400 & 150\end{bmatrix}\begin{bmatrix}50 \\ 20 \\ 40\end{bmatrix}\]

\[ = \begin{bmatrix}20000 + 6000 + 4000 \\ 15000 + 5000 + 3000 \\ 25000 + 8000 + 6000\end{bmatrix}\]

\[ = \begin{bmatrix}30000 \\ 23000 \\ 39000\end{bmatrix}\]

Hence, the total cost incurred by the organisation for three villages separately is

X: ₹30,000
Y: ₹23,000
Z: ₹39,000