The quality of air in an industrial region largely depends on the effluent emission from n plants. Each plant can use m different types of fuel. Suppose that the total energy needed at plant j is bj British thermal units per day and that eij is the effluent emission per ton of fuel type i at plant j. Further suppose that fuel type i costs ci dollars per ton and that each ton of this fuel type generates αij British thermal units at plant j. The level of air pollution in the region is not to extend b micrograms per cubic meter. Finally, let ?j be a meteorological parameter relating emissions at plant j to air quality at the region.
(a) 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 justification.
(b) How would you incorporate technology constraints that prohibit the use of certain mixes of fuel at certain plants? (Hint: consider the case where a specific fuel must be excluded from the mixes in a certain plant, and the case where two particular fuels cannot coexist in a given plant.)
(c) How could you insure equity among the plants? (Hint: consider placing a limit on the daily cost of energy per plant.)