Formulate an optimization problem to optimize the total cost of biological wastewater treatment plant. A

rectangular tank $($length x$1$ m$,$ width x$2$ m$,$ and height x$3$ m$)$ has been made for biological treatment of

wastewater $($batch process$).$ The sides and bottom of the tank cost Rs$.1200$ and Rs$.2500$ per m$2$ area,

respectively. The operating cost for the tank is Rs$.500$ for each batch of water treatment. A maintenance

cost of Rs$.100$ for every $10$ batch is required. Assuming that the tank will have no salvage value, find the

minimum cost for treatment of $1000$ m$3$ of wastewater. Assume the salvage value of the tank is zero after

$1000$ m$3$ of wastewater treatment. $($Dutta$,2016,$ p$.30)$