Problem 3 (20 Points; Adapted from Winston, 2004). 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 following table: From Warehouse 1 Warehouse 2 Customer 1 Customer 2 Customer 3 $12 $35 $25 $10 $52 $40 There is a penalty for each unmet unit of customer demand: With customer 1, a penalty of $90 is incurred; with customer 2, $80; and with customer 3, $110. Formulate a balanced transportation problem to minimize the sum of shortage and shipping costs, and use the AMPL minimum cost flow model (provided in class) to solve the transportation problem. (Note: For this problem, you should provide a drawing of the minimum cost flow network. Explain in words what nodes and arcs represent, and label nodes and arcs with the all relevant data. Provide a printout of your AMPL .dat file and your AMPL command session. Based upon your AMPL output, how many units should you ship from each warehouse to each customer?)