The U.S. has l mining regions where m coal types are produced for distribution to n consumer regions. Estimates for the following exist: the cost per ton of raw coal mined at a mining region for processing into a particular coal type for use at a consumer region ( cthun), the tons of raw coal available at each mining region (s), the yield in Btu of each ton of raw coal mined at a mining region for processing into a particular coal type (Q1m), and the demand in Btu of each coal type for each consumer region (dmn). The Environmental Protection Agency (EPA) wants to assess the impact on the U.S. coal market of different pollution control strategies and needs to determine how coal would be mined, processed, and distributed if the market seeks to minimize total cost. a) ( 3 points) What are the sets that you would need in your mathematical formulation? b) (3 points) What are the parameters that you would need in your mathematical formulation? c) (4 points) Define decision variables that would allow you to formulate this mathematical program. d) (3 points) Using the sets, parameters and decision variable(s) defined in parts a), b), and c), write down an expression for the objective function of cost minimization. (e) (6 points) Using the sets, parameters and decision variable(s) defined in parts a), b), and c), write down expressions for all of the constraints required in your mathematical program. (D) (8 points) Further, they want to enforce the rule that a maximum of Tlm different consumer regions can receive each coal type from each facility. How would you model this additional rule in your mathematical formulation? Hint: You may need to define additional decision variables. (9) 3 points) Explain what type of mathematical program (IP, MIP, LP, NLP, etc.) your final formulation above is, and why