Reference no: EM131100353
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:
(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 
(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. R
Prob. 11.2-1
Consider the following network, where each number along a link represents the actual distance between the pair of nodes connected by that link. The objective is to find the shortest path from the origin to the destination.
(a) What are the stages and states for the dynamic programming formulation of this problem?
(b) Use dynamic programming to solve this problem. However, instead of using the usual tables, show your work graphically (similar to Fig. 11.2). In particular, start with the given network, where the answers already are given for (sn) for four of the nodes; then solve for and fill in 
(B) and 
(O). Draw an arrowhead that shows the optimal link to traverse out of each of the latter two nodes. Finally, identify the optimal path by following the arrows from node O onward to node T.
(c) Use dynamic programming to solve this problem by manually constructing the usual tables for n = 3, n = 2, and n = 1.
(d) Use the shortest-path algorithm presented in Sec. 9.3 to solve this problem. Compare and contrast this approach with the one in parts (b) and (c). 1
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