$  Diet problem in Essence'
$  Standard Operations Research example.
$
$ Compare with the following models:
$ * MiniZinc: http://www.hakank.org/minizinc/diet1.mzn
$ * Choco: http://www.hakank.org/choco/Diet.java
$ * Comet: <a href="/comet/diet.co">diet.co
$ * ECLiPSE: <a href="/eclipse/diet.ecl">diet.ecl
$ * Gecode: <a href="/gecode/diet.cpp">diet.cpp
$ * Gecode/R: <a href="/gecode_r/diet.rb">diet.rb
$ * JaCoP: <a href="/JaCoP/Diet.java">Diet.java
$
$ Model created by Hakan Kjellerstrand, hakank@bonetmail.com
$ See also Hakan's Essence'/Tailor page: http://www.hakank.org/minion_tailor

language ESSENCE' 1.b.a

given n : int
given p : int
given price      : matrix indexed by [int(1..p)] of int(1..100)
given tlimits    : matrix indexed by [int(1..p)] of int(1..100)
given calories   : matrix indexed by [int(1..n)] of int(1..1000)
given chocolate : matrix indexed by [int(1..n)] of int(1..100)
given sugar      : matrix indexed by [int(1..n)] of int(1..100)
given fat        : matrix indexed by [int(1..n)] of int(1..100)

find x : matrix indexed by [int(1..p)] of int(0..1000)
find cost : int(0..10000)

minimising cost

such that
   cost = (sum i : int(1..p) . x[i]*price[i]),
   (sum i : int(1..n) . x[i]*calories[i])  >=  tlimits[1],
   (sum i : int(1..n) . x[i]*chocolate[i]) >=  tlimits[2],
   (sum i : int(1..n) . x[i]*sugar[i])     >=  tlimits[3],
   (sum i : int(1..n) . x[i]*fat[i])       >=  tlimits[4]