A sales manager wishes to assign four sales territories to four

Question

A sales manager wishes to assign four sales territories to four salespersons. The salespersons differ in their ability and skills and consequently the sales expected in each territory are different. The estimates of sales per month for each sales-person in different territories are given below:

Salespersons	Estimated Monthly Sales Territory
Salespersons	I	II	III	IV
A	20	40	45	30
B	50	40	55	40
C	45	40	42	50
D	48	50	42	45

Find the optimal assignment of the four salespersons to the four different territories and the maximum monthly sales.

09 Jan 2026

Answer :

Word Count : 412

The problem is an assignment problem with objective of maximizing total sales. Since the Hungarian method works for minimization, convert the given profit matrix into a loss matrix by subtracting each element from the largest entry in the table, which is 55. The sales matrix is A : (20, 40, 45, 30) B : (50, 40, 55, 40) C : (45, 40, 42, 50) D : (48, 50, 42, 45) The corresponding loss matrix (55 − sales) becomes A : (35, 15, 10, 25) B : (5, 15, 0, 15) C : (10, 15, 13, 5) D : (7, 5, 13, 10) Row ____ _____ _____ _____ ______ _________ ______.
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