1. The table below records transportation costs per unit of a product from origins 0 1, 0 2, 0 3 and 0 4 to destinations D1, D2, D3, D4 and D5• The capacities of the four origins are respectively 55, 45, 30 and 50 while the requirements of the five destinations are respectively 40, 20, 50, 30 and 40. Employing Vogel's Approximation method, or otherwise, make the initial allocations to the origins to satisfy the requirements of the destinations and test the optimality of these allocations. Use Modified Distribution method (MODI) for obtaining an optimal solution that would minimise the total cost of transportation.

Find the total cost implied by the solution. Is the solution unique? If not, find an alternative solution as well.

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Destination Origin Capacity D D D3 D4 D5 12 4 9 5 9 02 8 1 6 6 7 45 03 1 12 4 7 7 04 10 15 6 9 1 Luty 55 30 50 Requirement 40 20 50 30 40