Step-by-Step Solution
Topic: Matrix Multiplication & Applications
(I) COST MATRIX A
The cost per communication mode can be represented as a column matrix.
A =
| 15 |
| 10 |
| 25 |
(II) CONTACTS MATRIX B
The number of contacts for each village can be represented as a row in a matrix. Village X is the first row, and Village Y is the second row.
B =
| 100 | 150 | 110 |
| 150 | 200 | 150 |
(III) CALCULATING TOTAL COSTS
The total cost for each village is found by multiplying the contacts matrix B by the cost matrix A.
Total Cost = B × A
| 100 | 150 | 110 |
| 150 | 200 | 150 |
×
| 15 |
| 10 |
| 25 |
=
| (100×15) + (150×10) + (110×25) |
| (150×15) + (200×10) + (150×25) |
=
| 1500 + 1500 + 2750 |
| 2250 + 2000 + 3750 |
=
| 5750 |
| 8000 |
(III)(A) COST FOR VILLAGE X
The cost for Village X is the first element of the resulting matrix.
Cost for Village X = ₹ 5,750
(III)(B) COST FOR VILLAGE Y
The cost for Village Y is the second element of the resulting matrix.
Cost for Village Y = ₹ 8,000