problems 2 & 3 please

2 3000 Demand 1400 3200 5 2000 7 1400 Develop a network representation of the distribution system transportation problem). Consider the following network representation of a transportation problem: 2. Des Moines 25 14 Jefferson 30 City Kansas City 15 4 10 20 Omaha 3 St. Louis 10 Supplies Demands The supplies, demands, and transportation costs per unit are shown on the network. a. Develop a linear programming model for this problem; be sure to define the variable in your model. b. Solve the linear program to determine the optimal solution. 3. Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. Th company purchases natural gas from two companies: Southern Gas and Northwest Ga Chapter 6 Distribution and Network Models 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 follow- d. Recent residential and industrial growth in Butler County has the potential for increas ing demand by as much as 100 units. Which supplier should Tri-County contract with GloFish, Inc., has genetically engineered a species of fish that glows in normal lighting a ditions. The company believes the new fish will be a huge success as a new pet option for ing 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: 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 minimize total distribution costs. c. Describe the distribution plan and show the total distribution cost. to supply the additional capacity? 4. 07 a fish: on