\fProblem 6 (10 pts) 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. Table 1 gives the estimated increase in sales (in appropriate units) in each region if it were allocated various numbers of salespeople: Use dynamic programming to solve this problem. Show the problem by a network figure. Identify the resulting optimal path (or paths) through the network and the corresponding optimal solution (or solutions)