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<br />00055~ <br /> <br />q12 + qlS 1 1000 <br />~2 i 2000 <br />qlS i 2000 <br />~2' qlS 1 0 <br /> <br />The feaaible region defi~i~g the ranges of q12 and qlS that~satisfy all <br /> <br /> <br />the abo...e conatraints is sh01l'11 graphically u. Figure 21. <br /> <br />The objective is noy: <br /> <br />lIIini::i::e 7: .. 200 q12 + 100 Q1S <br /> <br />or <br /> <br />200 z <br />qlS'" - 100 q12 + 100 <br /> <br />For any value of z. the slope of the objective function is -2 On this <br /> <br />graph. Optt::i:i~g 7: lIIeans translating a line of slope -2 to the left as <br /> <br />fa: as possible. 'yhile still having at least one feasible point along <br /> <br />the line. This point IllUSt be opti::al. and is clearly: <br /> <br />. <br />~2 .. 0 <br /> <br />. <br />~S .. 1000 <br /> <br />for this e:ample. <br /> <br />Frca lIIass balance, this lIIeans that <br /> <br />. <br />qw .. 2000 <br /> <br />. <br />. ~ .. 1000 <br /> <br />Therefore, dellland node 1 receives its full allocation, end of period <br /> <br />storage in reso1"7oi: 1 is short. of the target by 1000, and de=and node 2 <br /> <br />recei...es nothing. The final storage of 1000 is then added to infloys <br /> <br />for the ne:t period and the ne:t period simnlation proceeds. Shifting <br /> <br />these priorities yould of course change the entire allocation. <br /> <br />E%te11.io11. <br /> <br />~annel'losses and evaporation yere neglected in this e:ample. <br /> <br />Their inclusion would lIIean that bounds wonld be adjusted, which lIIeans <br /> <br />that the lu.es in Figure 21 would be shifted in sOllie way, thereby possi- <br /> <br />b17 altering the solution (although not in this particular e:slllple). <br />