2. A company has four jobs (A, B, C and D) that it wishes to assign to four machines (W, X, Y and Z). Only one job can be assigned to each machine. The cost of assigning these jobs to each machine are as shown below:

Machine

W X Y Z
A 3 8 9 4
Job B 4 5 7 2
C 1 6 9 9
D 10 11 9 10


(a) Model the problem of as a linear program by clearly specifying the decision variables, objective function and the constraints.

(b) Solve the problem using Excel Solver to find an optimal assignment.
(c) Model the problem as a transportation model and get an initial solution

(d) Find an optimal solution starting from the initial solution in part (c)

(e) What is the increase in cost if the job D has to be assigned to Machine X for a technical reason.