Example $10\mathrm{.}4$ A company operates in four territories, and four salesmen available for an assignment. The territories are not equally rich in their sales potential. It is estimated that a typical salesman operating in each territory would bring in the following annual sales:

$\backslash$table$[[$Territory$,$:$,$I,II$,$III,IV$],[$Annual sales $($Rs$),$:$,1,26,000,1,05,000,84,000,63,000]]$

Assignment Problem

$321$

The four salesmen also differ in their ability. It is estimated that, working under the same conditions, their yearly sales would be proportionately as follows:

$\backslash$table$[[$Salesmen$,$A$,B,$C$],[$Proportion$,7,5,5]]$

If the criterion is maximum expected total sales, the intuitive answer is to assign the best salesman to the richest territory, the next best salesman to the second richest, and so on; verify this answer by the assignment technique. $[$Delhi Univ., MBA, $2004]$