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September 30th, 2013, 03:45 AM  #1 
Newbie Joined: Sep 2013 Posts: 5 Thanks: 0  Lagrangian Multiplier (discrete version)
Hi everyone, I have transformed my previously posted problem into discrete time (viewtopic.php?f=46&t=43103) : A school is trying to maximize its profits, which consist of the price charged for students of type i, p_i, times the number of students of type i, x_i, minus the Costs of having k customers, C(k). k is simply the sum of all customers x_i. Theta is the average ability of student all students. According to the solution, we can solve this by assuming we have an optimal and then forming the Lagrangian taking into account both constraints,i.e. the solution would be: where is the Lagrangian multiplier of the second constraint: 

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