We may view the optimal assignment problem of Chapter 1 as a transportation problem in the following way. Let a variable \(x_{i j}\) equal 1 if worker \(i\) is assigned to task \(j\), and 0 otherwise. There is a cost \(c_{i j}\) of assigning worker \(i\) to task \(j\).

(a) Formulate an objective function for the problem of minimization of total cost of assignment.

(b) Formulate constraints corresponding to the requirement that all workers have a distinct task.

(c) Solve the problem if the costs are as follows:

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C11 6, C12 == 4, C13 = 3, C21 = 6, C22 5, C23 8, C31 8, C32 2, C33 4.