4. [25%] A manufacturing company that specializes in sub-frames has three production facilities (A, B and C) and has secured four customers (1, 2, 3 and 4) for the coming year. The company has developed the following transportation network: 1 25,000 30 25,000 A 40 60 2 2 20,000 65 45 25,000 B 55 80 3 25,000 30,000 C 90/ 70 40 35 4 15,000 Each production facility has a production capacity, and each customer re- quires a set number of sub-frames. The cost (in $/sub-frame) to ship from a production facility to a customer is noted beside the corresponding arc. The company has concluded that it is not possible to ship from production facility A to customer 4. (a) Create the LP formulation of the problem. (b) Find the quantities and routes that will minimize the cost of transporta- tion. (c) The company wants to keep all its customers and realizes that it has to expand capacity to meet the current demand. Unfortunately it can only expand 1 production facility. Which facility should the company expand and by how much