Question
Cost per attempt: \[ \text{House call} = 50,\quad \text{Letter} = 20,\quad \text{Announcement} = 40 \] Number of attempts: \[ \begin{aligned} X &: (400, 300, 100) \\ Y &: (300, 250, 75) \\ Z &: (500, 400, 150) \end{aligned} \]
Solution
Step 1: Form Matrices
\[ A = \begin{bmatrix} 400 & 300 & 100 \\ 300 & 250 & 75 \\ 500 & 400 & 150 \end{bmatrix} ,\quad C = \begin{bmatrix} 50 \\ 20 \\ 40 \end{bmatrix} \]Step 2: Multiply
\[ \text{Total Cost} = A \times C \]Step 3: Calculate
Village \(X\): \[ 400×50 + 300×20 + 100×40 = 20000 + 6000 + 4000 = 30000 \] Village \(Y\): \[ 300×50 + 250×20 + 75×40 = 15000 + 5000 + 3000 = 23000 \] Village \(Z\): \[ 500×50 + 400×20 + 150×40 = 25000 + 8000 + 6000 = 39000 \]Final Answer
Village X cost = ₹30000
Village Y cost = ₹23000
Village Z cost = ₹39000