Northwest Gas 12 15 19 (a) Develop a network representation of this problem. (Submit a file with a maximum size of 1 MB.) Choose related (b) Develop u inear programing modes that can be used to determine the plan that will minimize total distribution costs Let Xu - amount shipped from Southern Gas to Hamilton * 12 amount shipped from Southern Gas to Butler *13 - amount shipped from southern Gas to Clarmont X21 amount shipped from Northwest Gers to Hamilton Xy - amount shipped from Northwest Go to Butler X23 - amount shipped from Northwest Gas te Clermont *12+ 3+ 21 + s.t. 11 + + * 12 + + X2 21 *22+ X23 3 + *22 + X23 X.2 + X22 X + * *111*12*132*2220 (c) Describe the distribution plan and show the total distribution cost. Optimal Solution Amount Cost Southern-Hamilton Southern-Butler $ Southern-Clermont $ Northwest-Hamilton $ Northwest-Butler $ Northwest-Clermont $ Total Cost $ (d) Recent residential and industrial growth in Butler County has the potential for increasing demand by 100 units ) Create an updated distribution plan assuring Southern Gas becomes the preferred supplier Distribution Plan with Southern Gas Amount Cost Southern-Hamilton $ Southern-Butler $ Southern-Clermont $ Northwest-Hamilton $ Northwest-Butler $ Northwest-Clermont $ Total Cost $ CID Create an updated distribution plan assuming Northwest Gas becomes the preferred supplier. Distribution Plan with Northwest Gas Amount Cost Southern-Hamilton $ Southern-Butler $ Southern-Clermont $ Northwest-Hamilton $ $ Northwest-Butler $ Northwest-Clermont $ Total Cost $ (ii) Which supplier should Tri-Courly contract with to soply the additional capacity? The Tri-County contract - le Select In-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural ges from tho companies: Southom Gas and Northwest Cas. Demand forecasts for the coming winter season are as folows: Harmilton County 400 units; Bater County, 200 urts; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, son 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 To From Hamilton Butler Clermont Southern Gas 10 20 15 Northwest Gas 12 15 18 (a) Develop a network representation of this problem. (Submit a file with a maximum size of 1 MB. Chi no lo colected (5) Develop a linear programming model that can be used to determine the plan that will minimize tatal distribution costs. Let *.. - amount shipped from Southern Gas tu Hamilton X., - amount shipped from southern Gas to Butler *.2 - amount shipped from Southern Gas to Clermont - amount shipped from Northwest Gas to Hamilton - amount shipped from Northwest Gas to Butiar Nya - amount shipped from Northwest Gas to Clermont + X22 + X) s.t. X.1 + *22 + 12 + X22 + X23 X 421 X 972 112 1 X3 * *.2:1). *2.22.2222 (c) Describe the distribution plan and show the total distribution Cost Optimal Solution Amount Cost Southern-Hamilton $ Southern-Butler $ Southern-Clermont $ Northwest-Hamilton $ Northwest-Butler $1 Northwest-Clermont $ $ $ Total Cost (d) Recent residential and industrial growth in Butler County has the potential for increasing demand by 100 units 10) Create an updated distribution plan assuming Southern Gas becomes the preferred supplier. Distribution Plan with Southern Gas Amount Cost Southern-Hamilton S Southern-Butler S Southern-Clermont S Northwest-Hamilton 5 Northwest-Butler 5 Northwest-Clermont S Total Cost Cresse an upcated distribution plan assuming Northwest Gas becomes the preterrec supplier Distribution Plan with Northwest Gas Amount Cost Southern-Hamilton S Southern-Butler Southern-Clermont s