Problem #2 (20 points) The quality of air in an industrial region largely depends on the effluent emission from 31 plants. Each plant can use m different types of fuel. Suppose that the total energy needed at. plant j is by British thermal units per day and that eg- is the efuent emission per ton of fuel type i at plant j. Further suppose that fuel type 1? costs C;- dollars per ton and that each ton of this fuel type generates (13' British thermal units at plant j. The level of air pollution in the region is not to extend 13'! micrograms per cubic meter. Finally, let )5;- be a meteorological parameter relating emissions at plant j to air quality at the region. Formulate the problem of determining the mix of fuels to be used at each plant as a linear program: clearly define the variables, and state the objective function and constraints with proper justication. Be sure that your formulation is written in implicit form