2. A transportation problem has the supplies at four sources and requirements at five destinations. The following table shows the cost of shipping one unit from a particular source to a particular destination:

The following feasible transportation pattern is proposed: x11 = 25, x 14 = 30, x 22 = 20, x 23 = 25, x 31 = 15, x 33 = 15, x43 = 10 and x45 = 40, and all other X;j = 0.
You are required to test whether this pattern has the least possible transportation cost. If so, how? If not, determine the optimal transportation pattern.

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Destination Source 1 2 3 4 5 1 15 7 2 11 4 3 4 15 4 13 18 9 200 8962 297 12 10 10 10 12 4