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# Mixed Integer Optimization

Posted 10 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 10 years ago
 x?Integers can be used to specify that a variable can take on only integer values. (from the documentation)
Posted 10 years ago
 NMinimize can make some variables integers and some real, but Minimize cannot.
Posted 10 years ago
 Thank you. Can you please let me know how to define variables within NMinimize