The quality of air in an industrial region largely depends on the effluent emiss

Question

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 ej 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 ay British thermal units at plantj. The level of air pollution in the region is not to extend b micrograms per cubic meter. Finally, let y 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 justification. Be sure that your formulation is written in implicit form

Explanation / Answer

object of the difficulty is to get together the supplies with smallest amount sum price of fuel. known so as to fuel kind i operating cost ci dollors for each load, so total price of i type fuel is ci*(Xi1 +Xi2+Xi3+.......+Xin)and sum price of every one kind of fuel determination exist outline of above look for all principles of i unreliable from 1 to m object purpose is twice outline of ci * Xij for all principles of i and j The constraint are concerning the height of air contamination (not to make better b micrograms for each cubic gauge) and Yj be a meteorological limit for emission at plant j plus sum power required at place j as bj in circumstances of British thermal unit. Given eij is emission of fuel type i at place j per ton, so total release at plant j is summation of eij Xij for all i untrustworthy from 1 to m and needs to be less than Yj for all values of j varying from 1 to n. Similarly if ti represent thermal unit for each ton of petroleum type i then outline of ti Xij ( i unreliable from 1 to m) will be the total power inspired at place j which be supposed to be equal to bj for all j unreliable from 1 to n. For gathering restraint of b micrograms per cubic measure extra in order about the total area in terms of cubic meters will be the denominator whereas the numerator is double draw round of eij * Xij for all principles of i and j. lastly non be short of of eagerness constraint of Xij as they represent quantity and can not be negative.

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