1) A company supplies goods to three customers, who each require 30 units. The company has two warehouses. Warehouse 1 has 40 units available, and warehouse 2 has 30 units available. The cost of shipping 1 unit from warehouse to customer are shown in the Table below. There is a penalty for each unmet customer unit of demand: With customer 1, a penalty cost of $90 is incurred; with customer 2, $80; and with customer 3, $110. To From Warehouse 1 Customer 1 $15 Warehouse 2 $10 Customer 2 $35 $50 Customer 3 $25 $40 a) Formulate a balanced transportation problem to minimize the sum of shortage and shipping costs. (Show the balanced transportation tableau). (5 pts.) b) Use Northwest Corner Method to find a bfs. (5 pts.) c) Use Transportation Simplex Method to solve this problem. Begin with the bfs you obtained from part b (NW corner method). (20 pts.) d) Use LINGO to solve this problem. Please print the LINGO model file and the solution file. (20 pts.)