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. Eaclh plant can use m different types of fuel. Suppose that the total energy needed at plant j is b, British thermal units per day and that ey 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 plant j. 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: justification. Be sure that your formulation is written in implicit form clearly define the variables, and state the objective function and constraints with proper

Explanation / Answer

answer:

• the quandary is comparable to transportion problem
• ,a individual class of linear encoding problem. arrangement of the trouble begin with defination of conclusion variables.let Xij be the amount of i kind firewood to be used at place j.
• as agreed in the query i changeable is worn for type of fuels that changeable from 1 to m as present are m types of fuels and j stand for plant life
• which are n numeral so j vary from 1 to n and Xij to ns of fuel sort i second-hand at place j takes the figure of a medium having m digit of row and n numeral of column.
• purpose of the trouble is to convene the obligation with maximum total rate of fuel.given that firewood type i expenses Ci dollers per ton,therefore whole price tag of i nature firewood is Ci(Xi1+Xi2+Xi3+.......+Xin) and
• full amount price tag of all types of fuels will be summing up of above appearance for all morals of i unreliable beginning 1 to m. goal task is binary précis of ci*Xij for all morals of i and j.
• the constrain are in relation to the point of air fumes (not to expand b micrograms per cubic meter) and Yij be a meteological limitation for production at stand j.
• and whole force desirable at fix j as Bj in conditions of boitish thermal units. given Cij is production of firewood type i and at place j per ton,therefore sum release at place j is rundown of Cij*Xij for all i varing from 1 to m and wants to be let than Yj for all principles of j anecdotal on or after 1 to n.
• simillarly if it represent thermal unit per ton of fuel i then summing up of Ti*Xij(i changeable from 1 to m) will be the whole enrgy obsessive at stand j
• which be supposed to be identical to bj designed for all j anecdotal from 1 to n for melt restriction of b micrograms per cubic meter extra informational regarding the whole region in provisos of cubic meters will be the denominato

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