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# solutions05 - 1 15.093J/2.098J Optimization Methods...

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1 15.093J/2.098J Optimization Methods Assignment 5 Solutions Exercise 5.1 BT, Exercise 10.2. The decision variables are x i , i = 1 , 20. x i = 1 if the player p i is selected; otherwise, p i =0. We have: The total number of players in the team is 12: 20 i =1 x i =12 The team has at least 3 play makers: 5 i =1 x i 3 The team has at least 4 shooting guards: 11 i =4 x i 4 The team has at least 4 forwards: 16 i =9 x i 4 The team has at least 3 centers: 20 i =16 x i 3 The team has at least 2 NCAA players: x 4 + x 8 + x 15 + x 20 2 Average rebounding statistics constraint: 20 i =1 r i x i 12 r Average assists statistics constraint: 20 i =1 a i x i 12 a Average scoring statistics constraint: 20 i =1 s i x i 12 s Average height statistics constraint: 20 h i x i 12 h i =1 Average defense ability statistics constraint: 20 d i x i 12 d i =1 Player p 5 is not in the team if the player p 9 is in the team: x 5 1 x 9 Player p 2 and p 19 can only be selected together: x 2 = x 19 At most 3 players from the same team ( p 1 ,p 7 ,p 12 ,p 16 ) are selected: x 1 + x 7 + x 12 + x 16 3 With these constraints, the problem for the coach is to maximize the scoring average or total the score 20 i =1 s i x i Exercise 5.2 BT, Exercise 10.4. Consider x ij is the number of module i we need to purchase in the year j ,where i = 1 , 5 representing module A, B, C, D, and complete engine respectively and j = 1 , 3. We have: x ij Z + for all i and j . We also need to know how many complete engines that will be broken into modules each year, let denote this quantity as x 6 j ,wehave , x 6 j Z + and x 6 j x 5 j .

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solutions05 - 1 15.093J/2.098J Optimization Methods...

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