$\backslash$table$[[,,,],[$From$,$To$,,],[$Southern Gas,$10,20,15],[$Northwest Gas,$12,15,18]]$

a$.$ Develop a network representation of this problem.

b$.$ Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs.

c$.$ Describe the distribution plan and show the total distribution cost.

d$.$ Recent residential and industrial growth in Butler County has the potential for increasing demand by as much as $100$ units. Which supplier should Tri$-$County contract with to supply the additional capacity?