Problem $1(25$ points$)$

A county chairwoman of a certain political party is making plans for an upcoming election. She

has received the services of four volunteer workers for precinct work, and she wants to assign

them to three precincts in such a way as to maximize their effectiveness. She feels that it would

be inefficient to assign a worker to more than one precinct, but she is willing to assign no

workers to any one of the precincts if they can accomplish more in other precincts. The table

below gives the estimated increase in the number of votes for the party's candidate in each

precinct if it were allocated various numbers of workers. Use dynamic programming to find the

optimal allocation.

a$)(7$ pts$.)$ Formulate the problem by defining stages, decision variables, states, state

transformation and recursive relationship.

$($b$)(18$ pts$.)$ Solve the problem using stage tables. Display the optimal policy.