14. The purchase manager, Mr Shah of the State Road Transport Corporation must decide on amounts of fuel to buy from three possible vendors. The corporation refuels its buses regularly at four depots within the area of its operations.

The three oil companies have said that they can furnish up to the following amounts of fuel during the coming month: 2, 75,000 litres by oil company 1; 5,50,000 litres by oil company 2; and 6,60,000 litres by oil company 3. The required amount of fuel is 1,10,000 litres at depot 1; 2,20,000 litres at depot 2:

3,30,000 litres at depot 3; and 4,40,000 litres at depot 4.

When the transportation costs are added to the bid price per litre supplied, the combined cost per litre of fuel from each vendor servicing a specific depot is shown here:

Determine the optimal schedule. Write the dual of the given problem and check optimal solution by using the dual.

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Company 1 Company 2 Company 3 Depot 1 5.00 4.75 4.25 Depot 2 5.00 5.50 6.75 Depot 3 4.50 6.00 5.00 Depot 4 5.50 6.00 4.50