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प्रश्न
A pharmaceutical company has four branches, one ea.ch at city A, B, C, D. A branch manager is to be appointed one at each city, out of four candidates P, Q, R and S. The monthly business deyending upon the city and the effectiveness of the branch manager in that city is given below :
| City | ||||
| A | B | C | D | |
| Monthly business (₹ lakh) | ||||
| P | 10 | 10 | 8 | 8 |
| Q | 12 | 15 | 10 | 9 |
| R | 11 | 16 | 12 | 7 |
| S | 15 | 13 | 15 | 11 |
Which manager should be appointed at which city so as to get the maximum total monthly business·?
उत्तर
Since it is a maximization problem . Subtract each of the elements in the table from the largest element.
Minimum element of each row is subtracted from every element in that row
Minimum element of each column is subtracted from every element in that column.
Since nwnber of lines covering all zeros is less than number of rows I columns.
∴ Subtract smallest uncovered element.
∴ Number of lines covering all zeros equal to number rows I column
∴ optimal solution has reached
Optimum allocation is as follows.
with total maximum business
8 + 12 + 16 + 15 = 51 (lakhs)
Assignment
P → D Q → A R → B S → C
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