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<br />" <br /> <br />reservoir, and lastly by demand node 2. Assume t~t there is zero flow <br /> <br />in the artificial spill link and the final storage link. Again assuming <br />mass balance is satisfied in all the artificial nodes. the problem is: <br /> <br />minimize -900~D -SOOqlS -700Q2D <br />subj ect to: <br /> <br />3000 - q12 - QlS - qlD ~ 0 <br />~2 + 1000 - Q2D . 0 <br />o i qlD i 2000 <br />o i ~D i 3000 <br />o i ~S i 2000 <br />o i qu i 4000 <br />Solving for qLD and q2D: <br />qlD . 3000 - q12 - qlS <br />~D . 1000 + qlZ <br />Substituting these into the objective' 'functio'u: <br /> <br />min -900(3000-Q12-QlS) <br />-800~S <br />-700(1000+qU) <br /> <br />Or <br /> <br />minimize 200~z + 100qlS <br />subject to: <br /> <br />o i (3000-~2-qlS) i 2000 <br />o i (lOOO~z) i 3000 <br />o i ~S i 2000 <br />o i ~Z i 4000 <br />!he only variables re=aining are q12 and qlS' !hese constraints can be <br />re"ritten as: <br /> <br />q12 + qlS i 3000 <br />