Please don't use an online calculator, they confuse me. The Ayatola Oil Company controls two oil fields. Field1 can produce up to 40 million barrels of oil per day, andfield 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; atfield 2, the cost is $2. Ayatola sells oil to two countries:England and Japan. The shipping cost per barrel is shownin Table 12. Each day, England is willing to buy up to 40million barrels (at $6 per barrel), and Japan is willing tobuy up to 30 million barrels (at S6.50 per barrel). Formulatea balanced transportation problem to maximize Ayatola'sprofits.TABLE 12To ($)From ($)EnglandJapanField 11Field 2212.

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.