Integer Linear Programming

Tom Cruise, Freddy Prinze Jr., Harrison Ford, and Matt LeBlanc be maro atomic number 53d on a desert island with Jennifer Aniston, Courtney Cox, Gwyneth Paltrow, and Julia Roberts. The compatibility measures in Table 52 omen how overmuch pleasure each pair off would perplex if they spent wholly their clipping together. The gladness earned by a couple is proportional to the cipher of time they unload together. Table 52 JACCGPJR TC7582 FP7894 HF3579 ML5567 a) Let Xij be the split of time that the ith man tops with the jth woman. The goal of the eight nation is to maximise the get along happiness of the people on the island. sound out an LP whose optimal solution get out yield the optimal cherish of the xijs. Input Output a)Explain why the optimal solution in graphic symbol (a) testament have four xij = 1 and twelve xij = 0. The optimal solution requires that each person spend all his or her time with one person of the other sex, so this dissolving agent is often referred to as the uniting Theorem. In order to increase happiness, each man will spend time with the close to compatible female that is gloss over available. Each person will stay with the same checkmate the entire day to maximize happiness.

If they were to change partners for a fraction of the day, the new partners would have raze happiness ratings and would cause the happiness rating to be let down than the maximum. If for a fraction of time we have combination of 4 couples that maximizes happiness, then it crumb be true for all day. That is why all Xij argon zero but 4 couples that are 1 (wh! ole day). b)Solve the business using assignment problem Input Output indite report to Manager: If Tom Cruise, Freddy Prinze Jr., Harrison Ford, and Matt LeBlanc are abandon on a desert island with Jennifer Aniston, Courtney Cox, Gwyneth Paltrow, and Julia Roberts, the maximum total happiness would be achieved if the following men spent their time with just one woman. Tom Cruise Gwyneth...If you want to get a broad(a) essay, order it on our website: BestEssayCheap.com

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