Question: a) Formulate the problem by defining stages, decision variables, states, state transformation and recursive relationship. b) Solve the problem using stage tables. Find the optimal

a) Formulate the problem by defining stages,

a) Formulate the problem by defining stages, decision variables, states, state transformation and recursive relationship.

b) Solve the problem using stage tables. Find the optimal policy. If more than one, find them all.

The number of crimes of each of a city's three police precincts depends on the number of patrol cars assigned to each precinct (see table below). For example, if 3 patrol cars are assigned to Precinct 2 the number of crimes in Precinct 2 will be 14. Seven patrol cars are available and at least one should be assigned to each precinct. Use dynamic programming to determine how many patrol cars should be allocated to each precinct to minimize the total number of crimes in the city. Precinct 1 Precinct 2 Precinct 3 Number of patrol cars assigned to precinct 1 12 19 14 2 10 17 11 3 8 14 8 4 5 5 6 3 12 11 5

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