(Scheduling Problems Viewed as Assignment Problems) A machine can be used to perform a subset of N given tasks over T time periods. At each time period t, only a subset A(t) of tasks can be performed. Each task j has value 
j (t) when performed at period t.
(a) Formulate the problem of finding the sequence of tasks of maximal total value as an assignment problem. Hint: Assign time periods to tasks.
(b) Suppose that there are in addition some precedence constraints of the general form: Task j must be performed before task j can be performed. Formulate the problem as an assignment problem with side constraints and integer constraints. Give an example where the integer constraints are essential.
(c) Repeat part (b) for the case where there are no precedence constraints, but instead some of the tasks require more than one time period