Using the excel template provided. Formulate a linear programming model (identify and define decision variables, objective function and constraints) that can be used to determine the plan that will minimize total distribution costs. Solve the LP problem using Excel Solver. Give the values of each decision variable and the objective function.

Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas. Demand forecasts for the coming winter season are as follows: Hamilton County, 400 units: Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars) are as follows: Hamilton From Southern Gas Northwest Gas To Butler 20 15 10 Clermont 15 18 12 B D E F G H Destination Butler Clermont Supply 2 3 4 Origin Hamilton 5 Southern Gas 6 Northwest Gas 7 Demand 8 9 10 Model 11 Minimize Total Cost 12 13 14 15 Origin Hamilton 16 Southern Gas 17 Northwest Gas 18 Total 19 20 Destination Butler Clermont Total