2. Figure 1 shows 5 pipelines (denoted by solid lines) under consideration by a natural gas company to move gas from its 2 fields to its 2 storage areas. The numbers on the arcs show the number of miles of line that would have to be constructed at $100,000 per mile. The figure also shows that storage facilities are both already connected to the company's main terminal through existing (dashed) lines. An estimated 800 million cubic feet must be shipped each year from field 1 to the terminal, and 600 million cubic feet must be shipped from field 2 to the terminal. Variable shipping costs are $2,000 per million cubic feet on each link of the network, and all the links have a capacity of 1 billion cubic feet. Formulate an integer program so that the company can realize a minimum total cost system for the required shipping. Figure 1: To #2 FI F1, 80 100 F2 S2 140 2. Figure 1 shows 5 pipelines (denoted by solid lines) under consideration by a natural gas company to move gas from its 2 fields to its 2 storage areas. The numbers on the arcs show the number of miles of line that would have to be constructed at $100,000 per mile. The figure also shows that storage facilities are both already connected to the company's main terminal through existing (dashed) lines. An estimated 800 million cubic feet must be shipped each year from field 1 to the terminal, and 600 million cubic feet must be shipped from field 2 to the terminal. Variable shipping costs are $2,000 per million cubic feet on each link of the network, and all the links have a capacity of 1 billion cubic feet. Formulate an integer program so that the company can realize a minimum total cost system for the required shipping. Figure 1: To #2 FI F1, 80 100 F2 S2 140