The sales manager for a publisher of college textbooks has six travelling salespeople to allocate 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 table below give the estimated increase in sales (in appropriate units) in each region if it were allocated various number of salespeople: Region Number of Salespersons Region Region Region 1 2 3 1 30 22 28 2 48 42 41 3 68 56 63 4 90 70 76 Use dynamic programming to find the optimal allocation. a) (8 pts.) Formulate the problem by defining stages, decision variables, states, state transformation and recursive relationship. b) (17 pts.) Solve the problem using stage tables. Display the optimal policy.