solve this question using:

a) leastcost method

b) northwest method

c) vogel's approximation method

PROBLEM 12 One major producer wants to buy raw material that does not exist in large stock. He needs to purchase 100 tones per week for the operation of the three factories, which have regular weekly requirements 40, 15 and 45 tons respectively. It is possible to satisfy these requirements if it obtains 40, 35 and 25 tons per week from three different suppliers. The cost of each unit of raw material is charged the same from any supplier, but the buyer must pay the costs of transportation for the three factories 6, 3.6 and 4.8 pounds for the first supplier, 2.4, 1.2 and 0.6 pounds for the second supplier and 6, 4.8 and 3.6 pounds for the third supplier, respectively. (a) How should the producer make the orders to minimize the total transportation cost and simultaneously meet requirements of the factory? (b) Assume that in the initial problem the requirement of the first factory is 50 tons per week, of the second factory 15 tons a week and of the third factory 35 tones per week. Determine the optimal solution and compare with that of the initial