1. A utilities company supplies natural gas to customers in three areas. The company purchases natural gas from two companies: Southern Gas and Northwest Gas. Demand forecasts for the coming winter season are Area 1, 400 units; Area 2, 200 units; and Area 3, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the areas vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars) are shown in Table 1. Table 1: Distribution costs From To Area 1 Area 2 Southern Gas 10 20 Northern Gas 12 15 Area 3 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. Solve the linear program to determine the optimal solution using CPLEX. d. Recent residential and industrial growth in Area 2 has the potential for increasing demand by as much as 100 units. Which supplier should the company contract with to supply the additional capacity?

1. A utilities company supplies natural gas to customers in three areas. The company purchases natural gas from two companies: Southern Gas and Northwest Gas. Demand forecasts for the coming winter season are Area 1, 400 units; Area 2, 200 units; and Area 3,300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the areas vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars) are shown in Table 1. Table 1: Distribution costs 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. Solve the linear program to determine the optimal solution using CPLEX. d. Recent residential and industrial growth in Area 2 has the potential for increasing demand by as much as 100 units. Which supplier should the company contract with to supply the additional capacity