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# The sales manager for a publisher of college textbooks has six traveling salespeople to assign to three different regions of the country.

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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