The Ayatola Oil Company controls two oil fields. Field 1 can produce up to 40 million barrels of oil per day, and field 2 can produce up to 50 million barrels of oil per day. At field 1, it costs $3 to extract and refine a barrel of oil; at field 2, the cost is $2. Ayatola sells oil to two countries: England and Japan. The shipping cost per barrel is shown in Table 12. Each day, England is willing to buy up to 40 million barrels (at S6 per barrel), and Japan is willing to buy up to 30 million barrels (at $6.50 per barrel). Formulate a balanced transportation problem to maximize Ayatola's profits. TABLE 12 To ($) From ($) England Japan Field 1 1 2 Field 2 1

If S1 and S2 represent the oil production at Field 1 and 2 respectively. So, S1= 40 and S2= 50 Let D1 and D2 represent the respective demand from England and Japan. England and Japan are willing to buy 40 million and 30 million barrels respectively. D1=40 and D2 = 30 Total Supply per day = S1 + S2 = 40 + 50 = 90 Total demand = D1+D2 =40+30 = 70 Hence, the demand is short by 20 million barrels. We can consider a dummy demand of 20 million barrels to eliminate the supply-demand gap, its transportation cost being zero. Suppose that , Let xij be the profit earned in transporting the oil from supply point i to demand point j. Since, the shipping cost per barrel from field 1 to England is $1, therefore the net profit will be, x21 = Purchasing cost per barrel by England – (shipping cost per barrel from field 1 to England + refinery cost per barrel at field 1) =6 - (1+3) =2 The shipping cost per barrel from field 2 to England is $2, therefore the net profit will be x12= Purchasing cost per barrel by England – (shipping cost per barrel from field 2 to England + refinery cost per barrel at field 2) = 6-(2+2) =2Similarly, The shipping cost per barrel from field 1 to Japan is $2, therefore the net profit will bex12 = Purchasing cost per barrel by Japan – (shipping cost/ barrel from field 1 to Japan + refinery cost/ barrel at field 1) = 6.5 -(2+3) = 1.5 The shipping cost per barrel from field 2 to Japan is $1, therefore the net profit will bex22 = Purchasing cost per barrel by Japan – (shipping cost/ barrel from field 2 to Japan + refinery cost/barrel at field 2) = 6.5 -(1+2) = 3.5 From the above data, the transportation problem is represented in the below table: The table represents the balanced transportation problem and its optimal solution.The Field 1 should supply 40 million barrels of oil to England and field 2 should supply 30 million barrels of oil to Japan to maximize the profit.