An allocation problem can be formulated as a linear programming problem with the introduction of decision variables. Suppose for example we have the following cost matrix for workers doing specific tasks:

Task 1 
Task 2 
Task 3 
Andrew 
9 
25 
17 
Boris 
11 
10 
49 
Charles 
27 
24 
13 
We can define decision variables x{ij} with the following properties:
Whereimplies Andrew,implies Boris andimplies Charles, and implies task 1, 2 or 3 respectively.
The objective is to minimise the total cost. We can write the objective function therefore as
The constraints are found by using the requirement that each worker be allocated to one task so that for each task, oneand the others equal 0 for that task. The requirement that just one worker be allocated to task 1 implies that
The requirement that just one worker be allocated to task 2 implies that
The requirement that just one worker be allocated to task 1 implies that