The Onenote Co. produces a single product at three plants for four customers. The three plants will produce 60, 80 and 40 units, respectively. The firm has made a commitment to sell 40 units to customer 1, 60 units to customer 2, and at least 20 units to customer 3. Both customers 3 and 4 also want to buy as many as possible. The sales price for each unit is $1200. The transportation cost associated with shipping a unit from plant i for sale to customer j is given in the following table.

	Customer 1	Customer 2	Customer 3	Customer 4
Plant 1	$800	$700	$500	$200
Plant 2	$500	$200	$100	$300
Plant 3	$600	$400	$300	$500

(a) Formulate the problem as a balanced transportation problem to maximize the net profit of the company (Hint: You can assume both customers 3 and 4 have extra demand of 60 units, and thus some dummy support is needed to meet the extra demand from these two customers, you should choose suitable penalty costs for committed sales and extra demand)

(b) Use the minimum cost method to find a starting solution

(c) Find the optimal solution of the problem using Simplex method.