The Burak 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 $2. Burak sells oil to two countries: England and Japan. The shipping cost ($) per barrel is as shown: Each day, England is willing to buy up to 40 million barrels (at $6 per barrel), and Japan is willing to buy up to 30 million barrels (at $6.50 per barrel). a) Formulate a balanced transportation problem to maximize Burak's profits. (2 marks) b) Then, find the optimal transportation solution to maximize the profit. (8 marks)