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May 15th, 2015, 05:25 AM  #1 
Newbie Joined: May 2015 From: Italy Posts: 1 Thanks: 0  linear programming  I have a question for 1 constraint
Hi All, I am developing software to solve a linear programming problem (for my team Athletic) and I can not find the mathematical representation for one of the constraints. The problem is the following: Maximize score of team presenting:  Scores of at least 12 different competitions  Maximum 18 scores  For each competition, you can submit as 2 scores  For every athlete can submit as 2 scores So we have a list of scores Score 1: High Jump, Athlete 1, Points: 500 (x1) Score 2: High Jump, Athlete 2 Points: 600 (x2) Score 3: Long Jump, Athlete 1, Points: 750 (x3) Score 4: Disco, athlete 3 Points: 600 (x4) Score 5: Disco, athlete 2 Points: 500 (x5) Score 6: High Jump, Athlete 4 Points: 700 (x6) etc. etc. etc. What I did was to consider each score as a variable to obtain an objective function max 500*x1 + 600*x2 + 750*x3 + 600*x4 + . + m*xn and then set various constraints on the variables so that they can take as value only 0 or 1 Constraint on the maximum number of competition: x1 + x2 + x3 + x4 + x5 + ... + xn<=18 Constraint on each athlete: x1 + x3<=2 .... x2 + x5<=2 Constraint on each competition: x1 + x2 + x6<=2 ... x4 + x5<=2 I can not find a mathematical representation of the constraint to take at least 12 different competitions Can anyone help me? Thank you and have a nice day 

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constraint, linear, programming, question 
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