Solution

Let

$C = \left[ \begin{array}{rrr} 25 & 44 & 36 \\ 28 & 41 & 40 \\ 23 & 50 & 35 \\ \end{array}\right]$be the cost matrix; $\large c_{ij}$= cost of assigning the $\large ith$contractor to the $\large jth$ Hall.

Optimal Assignment

Cost of an assignmet is the sum of n-entries of the cost matrix. No two of these entries come from the same row of the same column. An assignment with the smallest possible cost is called an optimal assignment.

NOTE: Note that if a number is added to all of the entries of any one row or column of a cost matrix then an optimal assignment for the resulting matrix is also an optimal assignment for the original cost matrix.