question_answer

To promote the making of toilets for women, an organisation 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 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 the three villages separately, using matrices. Write one value generated by the organisation in the society.

Answer:

Let A be the matrix that represent the number of attempts made in three villages X, V and Z and B be the matrix that represent the cost for each mode per attempt. Then, the matrices A and B are given by House calls Letters Announcements             \[A=\begin{matrix}    X  \\    Y  \\    Z  \\ \end{matrix}\left[ \begin{matrix}    400 & 300 & 100  \\    300 & 250 & 75  \\    500 & 400 & 150  \\ \end{matrix} \right]\]                                     Cost (in Rs.)             \[B=\begin{matrix}    \text{House}\,\,\text{calls}  \\    \text{Letters}  \\    \text{Announcements}  \\ \end{matrix}\left[ \begin{matrix}    50  \\    20  \\    40  \\ \end{matrix} \right]\] Now, the cost incurred by the organisation for three villages is given by             \[AB=\begin{matrix}    X  \\    Y  \\    Z  \\ \end{matrix}\left[ \begin{matrix}    400 & 300 & 100  \\    300 & 250 & 75  \\    500 & 400 & 150  \\ \end{matrix} \right]\,\,\,\left[ \begin{matrix}    50  \\    20  \\    40  \\ \end{matrix} \right]\]             \[=\begin{matrix}    X  \\    Y  \\    Z  \\ \end{matrix}\left[ \begin{matrix}    400\times 50+300\times 20+100\times 40  \\    300\times 50+250\times 20+75\times 40  \\    500\times 50+400\times 20+150\times 40  \\ \end{matrix} \right]\]\[=\begin{matrix}    X  \\    Y  \\    Z  \\ \end{matrix}\left[ \begin{matrix}    20000+6000+4000  \\    15000+5000+3000  \\    25000+8000+6000  \\ \end{matrix} \right]=\begin{matrix}    X  \\    Y  \\    Z  \\ \end{matrix}\left[ \begin{matrix}    30000  \\    23000  \\    39000  \\ \end{matrix} \right]\]       Thus, the total cost incurred by the organisation for the three villages X, Y and Z separately are Rs. 30000, Rs. 23000 and Rs. 39000, respectively. Value As society is conservative about the health of women, therefore this will force the people to make toilets, which will help to maintain hygenic condition in the society.