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# Mixed Integer Optimization

Posted 9 years ago
 Hello, I have a simple symbolic optimization model includes integer and real numbers Minimize[{-ax - bz - ct - f + n, n <= (ax + bz + ct + f) && n >= (ax + bz + ct + f) && 1 <= x <= 105 && 1 <= z <= 30 && 1 <= t <= 22 && 7500 < a && a <= b <= c && c <= 2*a && x + z + t <= 22 && x + z + t >= 22 && (ax + bz + ct) h <= f }, { a, b, c, h, x, t, z , n}]  the answer is {0, {a -> 7500, b -> 9000, c -> 12000, x -> 3/2, t -> 3/4, z -> 3/4, n -> f + tc + xa + zb}}  I need to know to define x,z,t as integers, any help is highly appreciated. Given that I am using latest Mathematica version where mixed integer supposed to be supported. wherever I define these variables as integers it will show an error. any idea? I am not expert, this is my first try with Mathematica.
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Posted 9 years ago
 NMinimize can make some variables integers and some real, but Minimize cannot.
Posted 9 years ago
 Thank you. Can you please let me know how to define variables within NMinimize
Posted 9 years ago
 x?Integers can be used to specify that a variable can take on only integer values. (from the documentation)