Question 2 [17 marks]. A power company operates three power generation plants. One is a wind plant, and the other two consume a combination of Fuel 1 and Fuel 2, emitting carbon dioxide in the process. In addition, all three plants require maintenance. The amount of fuel consumed (in Mg), maintenance required (in person-hours), carbon dioxide (CO2) emitted (in Mg), and power generated (in MWh) per day of operation is as follows: Maintenance Fuel 1 Fuel 2 CO2 Power Plant Required Required Required Emitted Produced 1 20 0 0 0 20 2 13 10 15 12 32 3 18 30 40 29 40 Each MWh of power can be sold at 121 and there is no limit on the amount that can be sold. Over its next planning period, the company has 230 person-hours for maintenance, 75 Mg of Fuel 1, and 90 Mg of Fuel 2 available. (a) Due to environmental regulations, they cannot emit more than 200Mg of CO2 in this period. The company wants to know how to operate its plants to generate as much revenue as possible (you may assume that there is no limit on the number of days a plant can operate in this period). Give a linear program that models this problem and state what each of your variables is meant to represent. You do not need to solve this program. [11] (b) Suppose now that the company can emit more than 200Mg of CO2, but now loses 55 of revenue for each Mg emitted after the first 200Mg because it must purchase CO2 credits. The other resource constraints remain as stated. The company now wants to know how to operate its plants to generate as much revenue as possible (you may assume that there is no limit on the number of days that a plant can operate in this period). Give a linear program that models this problem. You do not need to solve this program.