Please include excel models as well. Thank you

For each of the following 2 problems: - Clearly specify your decision variables, objective function and constraints. - If you draw the network or write the LP formulation by hand - make sure to scan it or take a picture and embed it in your word document or Excel file. ALL WORK (including Excel files) SHOULD BE SUBMITTED IN BLACKBOARD Problem \#1 (problem \# 3 in chapter 6) 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 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: (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) Enter your model into Excel. Use the solver to determine the optimal solution: describe the distribution plan and show the total distribution cost. (d) (variation on question from text) Recent residential and industrial growth in Butler County has the potential for increasing demand by as much as 100 units. Describe how you would change the model you developed in (a) and (b) and then use Excel solver to determine the distribution plan and total distribution cost for this scenario