Question
Cost per contact (in paise): \[ A = \begin{bmatrix} 140 \\ 200 \\ 150 \end{bmatrix} \] 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
\[ \text{Total Cost} = B \times A \] \[ = \begin{bmatrix} 1000 & 500 & 5000 \\ 3000 & 1000 & 10000 \end{bmatrix} \begin{bmatrix} 140 \\ 200 \\ 150 \end{bmatrix} \]Step 2: Calculate
City \(X\): \[ 1000×140 + 500×200 + 5000×150 \] \[ = 140000 + 100000 + 750000 = 990000 \text{ paise} \] City \(Y\): \[ 3000×140 + 1000×200 + 10000×150 \] \[ = 420000 + 200000 + 1500000 = 2120000 \text{ paise} \]Step 3: Convert to Rupees
\[ X = ₹9900,\quad Y = ₹21200 \]Final Answer
Total cost in city \(X\) = ₹9900
Total cost in city \(Y\) = ₹21200
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