The Omega Pharmaceutical firm has five salespersons, whom the firm wants to assi

Question

The Omega Pharmaceutical firm has five salespersons, whom the firm wants to assign to five sales regions. Given their various previous contacts, the sales persons are able to cover the regions in different amounts of time. The amount of time (days) required by each salesperson to cover each city is shown in the following table:

Salesperson

Region (days)

                A   B    C     D    E

1              20 10 12 10 22

2             14 10 18 11 15

3             12 13 19 11 14

4             16 12 14 22 16

5             12 15 19 26 23

Which salesperson should be assigned to each region to minimize total time? Identify the optimal assignments and compute total minimum time. Fill in blanks below

DV Sales-person A B C D E Assignment 1 = 1 2 = 1 3 = 1 4 = 1 5 = 1 Constraints = = = = = Region assigned 1 1 1 1 1 Objective Minimize Time

Explanation / Answer

This is the given table.

Now we perform Row operations by subtracting all the smallest numbers in the rows from each element in that row.

We still haven't found an optimal and a feasible solution. Now we move to column opperations and subtract the smallest element in each column from each element in that column.

Column 3 and 5 will be modified.

We then are able to get the optimal solution,

Thus, the optimal assignment will be:

A = Zone 5

B = Zone 2

C = Zone 4

D = Zone 1

E = Zone 3

Hope this helps.

A B C D E 1 20 10 12 10 22 2 14 10 18 11 15 3 12 13 19 11 14 4 16 12 14 22 16 5 12 15 19 26 23

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