First develop the problem formulation, then use Solver to solve the network model and answer problem questions.

3. 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 writton: 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: To From Hamilton Butler Clermont Southern Gas 10 20 15 Northwest Gas 12 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 minimizo total distribution costs. 4: Describe the distribution plan and show the total distribution cost. d. Recent residential and industrial growth in Butler County has the potential for increasing demand by as much as 100 units. Which supplor should Tri-County contract with to supply the additional capacity? Preme Court Avery and Baker can be who want to remove a wont Cambol som de ant ready to be forcent of 10 hours over the next four the company has turn process the home to the cents over the week periodo Client Hours A 180 1 75 c 100 D 8 Hourly rates vary for the consultant-lent combinand are based on a concluding type and the conseca Theta dos per horech concerto follows Client A c Consultant D Avery 100 125 100 115 120 115 120 155 Campo 150 130 140 Develop a work representation of the problem Formulate the problem as a near program with the position provide the short should be scheduled for each to main contra in the total bing? Forbot Corporations in a contracto supply or for at forsproduced by the A Corporation Agentum te region tour in wood acolo los Angelo and SL Paul. Plane call form fotowing number onthousands of meriton to be produced the Botion 50 Dallas 70 Los Ang 00 St. Paul Forbell's me plantare capable of the motors. The producties on the show 100 Allant 100 Chicago 100 Because of varying production and transportation cont, me protein occhio 1000 untrends on which plant role and which deration with the owner the accounting department states of the properties will be made in lots of 10 Shipper To Dallas Boston Los Angeles St. Paul Produced At 13 11 Denver 10 12 17 20 A 16 18 Chicago 17. Scott and Associates, Inc., is an accounting firm that has three new clients. Project leaders will be assigned MSELFtest to the three clients. Based on the different backgrounds and experiences of the leaders, the various leader-client assignments differ in terms of projected completion times. The possible assignments and the estimated completion times in days are as follows: Client Project Leader 1 2 2 3 3 Jackson 10 16 32 Ellis 14 22 40 Smith 22 24 34 a. Develop a network representation of this problem. b. Formulate the problem as a linear program and solve. What is the total time required? 24. In the original Gorman Construction Company problem, we found the shortest distance from the office (node 1) to the construction site located at node 6. Because some of the roads are highways and others are city streets, the shortest-distance routes between the office and the construction site may not necessarily provide the quickost or shortest-time route. Shown here in the Gorman road network with travel time rather than distance Find the shortest route from Gorman's office to the construction site at node 6 if the objective is to minimize travel time rather than distance Tradi 15