The sales manager for a publisher of college textbooks has

six traveling salespeople to assign to three different regions of the

country. She has decided that each region should be assigned at

least one salesperson and that each individual salesperson should

be restricted to one of the regions, but now she wants to determine

how many salespeople should be assigned to the respective regions

in order to maximize sales.

The following table gives the estimated increase in sales (in

appropriate units) in each region if it were allocated various numbers

of salespeople:

Region

Salespersons 1 2 3

1 35 21 28

2 48 42 41

3 70 56 63

4 89 70 75

(a) Use dynamic programming to solve this problem. Instead of

using the usual tables, show your work graphically by constructing

and filling in a network such as the one shown for

Prob. 11.2-1. Proceed as in Prob. 11.2-1b by solving for f n*(sn)

for each node (except the terminal node) and writing its value

by the node. Draw an arrowhead to show the optimal link (or

links in case of a tie) to take out of each node. Finally, identify

the resulting optimal path (or paths) through the network

and the corresponding optimal solution (or solutions).

(b) Use dynamic programming to solve this problem by constructing

the usual tables for n 3, n 2, and n 1.

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