SealCo is an automobile manufacturer and at the beginning of April, SealCo wants to come up with a production plan to meet the following demands for a car: April, 30 units; May, 30 units; June, 20 units. When SealCo cannot meet the demand for a specific month, it may be backlogged at a cost of $5/unit/month. All the backlogged demand must be met at most during June (at the end of the 3-months planning horizon), then a backlogging cost of 5(2) = $10 is incurred. SealCo’s monthly production capacity and unit production cost during each month are given in table below. A holding cost of $20/unit is charged due to the inventory at the end of each month. 

Month     Production Capacity (units) Unit Production Cost 

April 30                                      $100 

May 30                                       $120

June 30                                       $110 

(a) Construct a transportation tableau for the problem. Is this a balanced TP? Why or why not? Explain. Also show the cost calculations on the transportation tableau.

(b) Formulate a balanced transportation problem that could be used to determine how to minimize the total cost (including backlogging, holding, and production costs) of meeting demand. 

(c) Solve the problem by using IBM ILOG CPLEX Optimization Studio. Write down the optimal solution and make comments. Submit also your OPL output with your homework.