- Four sales representatives ( \(R _ { 1 } , R _ { 2 } , R _ { 3 }\) and \(R _ { 4 }\) ) are to be sent to four areas ( \(A _ { 1 } , A _ { 2 } , A _ { 3 }\) and \(A _ { 4 }\) ) such that each representative visits one area. The estimated profit, in tens of pounds, that each representative will make in each area is shown in the table below.
| \cline { 2 - 5 }
\multicolumn{1}{c|}{} | \(A _ { 1 }\) | \(A _ { 2 }\) | \(A _ { 3 }\) | \(A _ { 4 }\) |
| \(R _ { 1 }\) | 37 | 29 | 44 | 51 |
| \(R _ { 2 }\) | 45 | 30 | 43 | 41 |
| \(R _ { 3 }\) | 32 | 27 | 39 | 50 |
| \(R _ { 4 }\) | 43 | 25 | 51 | 55 |
Use the Hungarian method to obtain an allocation which will maximise the total profit made from the visits. Show the state of the table after each stage in the algorithm.