$11\mathrm{.}2-2.$ Layla Brown is the sales manager for a publisher of college textbooks. She has six traveling

salespeople to assign to three different regions of the country. Layla 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 next table gives the estimated increase in sales $($in appropriate units$)$ in each region if it were

allocated various numbers of salespeople: $($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

$\frac{?}{{?}_{\frac{?}{?}}}$ Prob. $11\mathrm{.}2-1.$ Proceed as in $\frac{?}{{?}_{\frac{?}{?}}}$ Prob. $11\mathrm{.}2-1b$ by solving for $f_n^{*}(s_n)$ 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 $n=1$