Operation Research LP help

A steel company transfers steel from three factories (1, 2 and 3) to three construction sites (A, B and C). The production capacities of the three factories (1, 2 and 3) are 150, 175 and 275 tons, respectively. While the three construction sites (A, B and C) have requirements of 200, 100, and 300 tons, respectively. The table below summarizes the shipment costs per ton from each factory to each construction site.

	Site A	Site B	Site C
Factory 1	C1A	C1B	C1C
Factory 2	C2A	C2B	C2C
Factory 3	C3A	C3B	C3C

Where C1A = 1 + [(134077) mod (1)], C1B = 1 + [(134077) mod (3)],

C1C = 1 + [(134077) mod (5)], C2A = 1 + [(134077) mod (7)], C2B =

1 + [(134077) mod (9)], C2C = 1 + [(134077) mod (8)], C3A = 1 + [(134077) mod (6)], C3B = 1 + [(134077) mod (4)], and C3C = 1 + [(134077) mod (2)].

a) Determine a basic feasible solution using the following three methods:

i. The North-west corner method.

ii. The Least-cost method, and

iii. The Vogel approximation method.

b) Determine the optimal solution using the steppingstone method. Start using the Vogel’s approximation feasible solution.

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