Kiya Grain Company is engaged in grain distribution. The company currently has three distribution centers in Washington DC, Boston, and New york. The company procures grain from three suppliers located in Atlanta, Nevada, and phoenix. Procurement cost for the company includes both purchase price and transportation cost. The supplier in Atlanta sells grain for a price of Birr 1000 per quintal. Transportation costs from Atlanta to the three distribution centers are Birr 18, 20, and 41 respectively. The Nevada supplier sells grain for Birr 1140 per quintal and additional transportation cost to the three distribution centers from Nevada are Birr 27, 22, and 36, respectively. The phoenix supplier sells grain for Birr 1060 per quintal and charges a transportation costs of Birr 32, 28 and 24, respectively for shipments to the 3 centers. The capacities of the three suppliers are 2000 units, 1500 units and 1200 quintals, respectively. The demands in the three centers are 1700, 2100 and 1800 units, respectively.
a) How much quintals of grain should be sent from each source to each destination to minimize total cost of distribution? (Use NW corner and MODI to obtain a solution)
b) Suppose that the Nevada supplier will be advantageous if Kiya Grain can let it make larger shipments to the Washington DC center. But Kiya will allow this only if either this plan reduces or doesn’t affect the optimal cost of the original schedule. How much special price concession should the Nevada supplier offer for shipments to the Washington DC center so that Kiya can be willing to rearrange its schedule?
c) Suppose that transportation costs increased by 20 birr from every source to every destination, should Kiya’s management change its distribution schedule?
