(Transportation problem with shortage)

A company supplies goods to 3 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: a penalty cost of $90 is incurred with customer 1, $80 is incurred with customer 2, $110 is incurred with customer 3. Formulate the problem as a transportation problem in order to minimize the sum of shortage and shipping costs.

From Customer 1 Customer 2 Customer 3 Supply Warehouse 1 $15 $35 $25 40 Warehouse 2 $10 $50 $40 30 Demand 30 30 30 Penalty cost $90 $80 $110