kWh in increments of 10 kWh. Develop a graph with profit on the vertical axis and required ending battery level on the horizontal axis. Given that Star has not forecasted LMPs for periods 11, 12, and so on, what ending battery level do you recommend that Star use in its optimization model?Chapter 10Problem 3 (8 points)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 thecoming 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: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. d.Recent residential and industrial growth in Butler County has the potential for increasing demand by as much as 100 units. Which supplier should Tri-County contract with to supply the additional capacity?Problem 7 (10 points)Aggie Power Generation supplies electrical power to residential customers for many U.S. cities. Its main power generation plants are located in Los Angeles, Tulsa, and Seattle. The following table showsAggie Power Generation’s major residential markets, the annual demand in each market (in

megawatts or MW), and the cost to supply electricity to each market from each power generation plant (prices are in $/MW).a.If there are no restrictions on the amount of power that can be supplied by any of the power plants, what is the optimal solution to this problem? Which cities should be supplied by which power plants? What is the total annual power distribution cost for this solution?b.If at most 4000 MW of power can be supplied by any one of the power plants, what is the optimal solution? What is the annual increase in power distribution cost that results from adding these constraints to the original formulation?