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Unformatted text preview: practical algorithm. Lets ASSUME for a moment that we have all the possible (P 1 i ,P 2 i ) and (Q 1 i , Q 2 i ). Then it follows from convexity of each of the constraint sets that any linear combinations of the (P 1 i ,P 2 i ) offers is also feasible o i.e. for any set of i such that i = 1 an offer i (P 1 i ,P 2 i ) is also feasible any linear combinations of the (Q 1 i ,Q 2 i ) offers is also feasible o i.e. for any set of i such that i = 1 an offer i (Q 1 i ,Q 2 i ) is also feasible Thus any solution (P 1 , P 2 ) can be rewritten as i (P 1 i ,P 2 i ), or P 1 = i P 1 i and P 2 = i P 2 i Similarly we can rewrite Q 1 = i Q 1 i and Q 2 = i Q 2 i Substituting in the 2Plant model we obtain Max 90 i P 1 i + 80 i P 2 i + 70 i Q 1 i + 60 i Q 2 i subject to 8 i P 1 i + 6 i P 2 i + 7 i Q 1 i + 5 i Q 2 i 80; i =1 i = 1 i , i 0...
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 Spring '11
 Daniel

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