Question
Cost per contact (in paise): \[ A = \begin{bmatrix} 40 \\ 100 \\ 50 \end{bmatrix} \] Number of contacts: \[ B = \begin{bmatrix} 1000 & 500 & 5000 \\ 3000 & 1000 & 10000 \end{bmatrix} \] Find total cost in cities \(X\) and \(Y\).
Solution
Step 1: Multiply
\[ \text{Total Cost} = B \times A \] \[ = \begin{bmatrix} 1000 & 500 & 5000 \\ 3000 & 1000 & 10000 \end{bmatrix} \begin{bmatrix} 40 \\ 100 \\ 50 \end{bmatrix} \]Step 2: Calculate
City \(X\): \[ 1000×40 + 500×100 + 5000×50 \] \[ = 40000 + 50000 + 250000 = 340000 \text{ paise} \] City \(Y\): \[ 3000×40 + 1000×100 + 10000×50 \] \[ = 120000 + 100000 + 500000 = 720000 \text{ paise} \]Step 3: Convert to Rupees
\[ X = ₹3400,\quad Y = ₹7200 \]Final Answer
Total cost in city \(X\) = ₹3400
Total cost in city \(Y\) = ₹7200