help please, it would help if you could show the answers directly

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. 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.) Choose File No file chosen This answer has not been graded yet. (b) Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs. Let X11 = amount shipped from Southern Gas to Hamilton X 12 = amount shipped from Southern Gas to Butler X13 = amount shipped from Southern Gas to Clermont 21 amount shipped from Northwest Gas to Hamilton X22 = amount shipped from Northwest Gas to Butler X23 = amount shipped from Northwest Gas to Clermont Min + 1X12 + 1X21 1X13 + 1X22 + 1 X23 s.t. X11 X2 + X 13 X22 + X23 X21 X21 VI VIII II X 11 + X12 + X22 X13 + X23 = * 11 * 12X13, X21X22X232 0 (C) Describe the distribution plan and show the total distribution cost. Optimal Solution Amount Cost Southern-Hamilton 300.00 s 3000 Southern-Butler s Southern-Clermont $ Northwest-Hamilton $ Northwest-Butler $ Northwest-Clermont 300.00 $ 4500 Total Cost $ 13,200.00 (d) Recent residential and industrial growth in Butler County has the potential for increasing demand by 100 units. (i) Create an updated distribution plan assuming Southern Gas becomes the preferred supplier. Distribution Plan with Southern Gas Amount Cost Southern-Hamilton 200 x s 2000 X Southern-Butler 0 s 0 Southern-Clermont 300 $ 4500 Northwest-Hamilton 200 X $ 2400 X Northwest-Butler 200 X $ 3000 X Northwest-Clermont 0 so Total Cost $ 11900 X (d) Recent residential and industrial growth in Butler County has the potential for increasing demand by 100 units. (1) Create an updated distribution plan assuming Southern Gas becomes the preferred supplier. Distribution Plan with Southern Gas Amount Cost Southern-Hamilton 200 x $ 2000 X Southern-Butler 0 0 Southern-Clermont 300 $ 4500 Northwest-Hamilton 200 X $ 2400 X Northwest-Butler 200 X $ 3000 x Northwest-Clermont 0 SO Total Cost $ 11900 X (ii) Create an updated distribution plan assuming Northwest Gas becomes the preferred supplier. Distribution Plan with Northwest Gas Amount Cost Southern-Hamilton S 10 x Southern-Butler 200 X $ 20 X Southern-Clermont 300 S 15 1x Northwest-Hamilton 400 X $ Northwest-Butler S 15 s x Northwest-Clermont $ 18 X Total Cost $ 900 x (iii) Which supplier should Tri-County contract with to supply the additional capacity? The Tri-County contract should go to the supplier with the lowest * cost, i.e. Southern Gas x