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Homework answers / question archive / Suppose that a salesman has potential customers in three different countries, and he can make at most 2 visits in total

Suppose that a salesman has potential customers in three different countries, and he can make at most 2 visits in total. Besides, he knows that if he can advertise prior to his visits he can increase the profit he can make. Hence, he allocates an advertising budget that can be used in only one of the countries. His profit estimates for every country are given in the following tables, as a function of the number of visits ( x ) and if advertising is done ( y) in that country. He wants to determine an optimal allocation policy for his two resources so that his total profit is maximized.

Country 1Adv (y) Count Adv. 0 (y) 1 Country 3 Adv. 0 (y) 1 0 I 0 c U1 0 0 2 0 isits isits 1 1 4 isits 121 2 2 4 6 4 7

a)Define the stages, decision variables, and states explicitly. b) Define an appropriate DP recursion and boundary conditions. c) Determine the salesman's optimal policy and earnings. Show all your calculations.