ABC Coop owns a steam-turbine power-generating plant. Because ABC is rich in coal deposits, the plant generates its steam from coal. This, however, may result in emission that does not meet the Environmental Protection Agency (EPA) standards. EPA regulations limit sulfur dioxide discharge to 2000 parts per million per ton of coal burned and smoke discharge from the plant stacks to 20 lb per hour. The Coop receives two grades of pulverized coal, C1 and C2, for use in the steam plant. The two grades are usually mixed together before burning. For simplicity, it can be assumed that the amount of sulfur pollutant discharged (in parts per million) is a weighted average of the proportion of each grade used in the mixture. The following data is based on the consumption of 1 ton per hr of each of the two coal grades. Coal grade Sulfur discharge in parts per million 1800 Smoke discharge in Ib. per hour 2.0 Steam generated in Ib. per hour 12000 C1 C2 2090 0.8 10000 a. e. a. Formulate the LP model (clearly state your variables and constraints). (3pts) b. b. Determine the optimal ratio for mixing the two coal grades using the graphical method (state the ratio and the optimum objective function). (5pts) C. c. Find the feasible region by making it a shaded area. (1pt) d. d. Find all corner points by marking them with capital letters, i.e., A, B, etc. (1pt) e. What are the binding constraints for the optimum? (1pt) f. f. What are the constraints (if any) that if we change it a little bit won't affect the optimum? (1pt) g. g. Find only the four basic solutions found in the graphical solution (b) and their corresponding basic variables and non-basic variables and determine if they are basic feasible solutions or not. (5pts) h. h. Determine the effect of relaxing the smoke discharge limit by 1 lb on the amount of generated steam per hour (using graphical method). (3pts)