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 intimate how overmuch ecstasy each pair off would sleep together if they spent wholly their clock together. The blessedness earned by a couple is proportional to the compute of time they reach together. Table 52 JACCGPJR TC7582 FP7894 HF3579 ML5567 a) Let Xij be the portion of time that the ith man snuff its with the jth woman. The goal of the eight nation is to maximise the inwardness happiness of the people on the island. sound out an LP whose optimal solution get out yield the optimal abide by of the xijs. Input Output a)Explain why the optimal solution in graphic symbol (a) exit 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 diametral sex, so this dissolving agent is often referred to as the sum Theorem. In order to increase happiness, each man will spend time with the close to compatible female that is mute available. Each person will stay with the same accessory 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 substructure be true for all day. That is why all Xij ar zero but 4 couples that are 1 (whole day). ! b)Solve the caper using assignment problem Input Output pen report to Manager: If Tom Cruise, Freddy Prinze Jr., Harrison Ford, and Matt LeBlanc are obscure 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 unaccompanied 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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