Question $in$ operation management $..$Please formulate the following as a linear program to determine the mix of fucls to

be used at each plant to minimize fuel costs:

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 $b_j$ BTUs per day and that $c_{jj}$ is the effuent emission per ton

of fuel type $i$ at plant $j.$ Further, suppose that fuel type i costs $c_4$ dollars per ton

and that each ton of this fuel type generates ${}_{ij}$ BTUs at plant $j.$ The level of air

pollution in the region is not to exceed $b$ micrograms per cubic meter. Finally, let ${}_j$

be a meteorological parameter relating emissions at plant $j$ to air quality in the region.