A cement company has three factories which manufacture cement which is then transported to four distribution centres. The quantity of monthly production of each factory, the demand of each distribution centre and the associated transportation cost per quintal are given as follows:

(i) Suggest the optimal transportation schedule.
(ii) Is there any other transportation schedule which is equally attractive? If so, write that.
(iii) If the company wants at least 5,000 quintals of cement are transported from factory C to distribution centre Y. will the transportation schedule be any different? If so, what will be the new optimal schedule and the effect on cost?
(iv) Suppose the company desires to send at most 500 quintals of cement from factory C to distribution centre Y. what will the optimal schedule be? Also, obtain the total transportation cost in such a case.
(v) The monthly production at factory C and the monthly demand at distribution centre X increase by 1,000 quintals each. What effect will it have on the optimal solution and on the total cost?

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Factories Monthly Demand (in quintals) Distribution Centres Monthly Production W Y Z AB 10 8 7 9 15 10 14 55 4 (in quintals) 7,000 8 8,000 8 10,000 6,000 6,000 8,000 5,000