Consider an assignment problem with an n by n cost matrix C with entries cij that denote the cost of assigning worker i to job j. Let , Rn be given and matrix C with entries c ij is obtained by setting: c ij = cij i j . (a) (4 points) Prove that solving the assignment problem with C will give the optimal solution to the problem with C. (b) (3 points) What would be difference between the objective values of the two problems? (c) (3 points) What would be such an , Rn and the corresponding C that you would obtain after the initial 2 steps of the Hungarian algorithm (up to the step when you start looking for 0-covers) for the following cost matrix? C = 11 7 2 27 20 5 21 7 12