For organizing four world cup cricket matches, cricket clubs of five cities have sent their proposals. The earnings from each match in each city are likely to be different because of the participating teams and local support they enjoy. The expected revenues in lakhs of rupees are as given in following table. How the matches should be assigned to various cities to maximize the expected revenue. -

Here one column is unbalanced, so we add fifth column with zero values.

This problem is of maximization, so covering it to minimization type by subtracting biggest value from table from each value.

Applying Row operation

Applying column operation as well as assigning jobs

No. of allocation not equal to no. of rows, so this is not feasible solution, so moving towards optimality.

Here we will draw four lines to cover all zero’s and crossed zero’s. Minimum uncovered value is 3. Subtracting 3 from all uncovered values & adding ‘3’ at the junction where two lines cross each other.

No. of allocations are not equal to no. of rows. Here we can’t draw four lines which will cover all zero’s and crossed zero’s. Therefore assigning in same matrix by priority rule Right-Lest & Top-Bottom.

No. of allocation = No. of rows

It is a feasible solution. No match for city ‘C’, since fifth column was dummy column.