Unformatted text preview: practical algorithm. Let’s 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 µ i such that Σµ i = 1 an offer Σµ 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 λ i such that Σλ i = 1 an offer Σλ i (Q 1 i ,Q 2 i ) is also feasible Thus any solution (P 1 , P 2 ) can be rewritten as Σµ i (P 1 i ,P 2 i ), or P 1 = Σµ i P 1 i and P 2 = Σµ i P 2 i Similarly we can rewrite Q 1 = Σλ i Q 1 i and Q 2 = Σλ i Q 2 i Substituting in the 2Plant model we obtain Max 90 Σµ i P 1 i + 80 Σµ i P 2 i + 70 Σλ i Q 1 i + 60 Σλ i Q 2 i subject to 8 Σµ i P 1 i + 6 Σµ i P 2 i + 7 Σλ i Q 1 i + 5 Σλ i Q 2 i ≤ 80; Σµ i =1 Σλ i = 1 µ i , λ i ≥ 0...
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This note was uploaded on 07/10/2011 for the course MIE 376 taught by Professor Daniel during the Spring '11 term at University of Toronto.
 Spring '11
 Daniel

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