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-----------------------------------------------------------------------------
-- |
-- Module : Documentation.SBV.Examples.Optimization.LinearOpt
-- Copyright : (c) Levent Erkok
-- License : BSD3
-- Maintainer: erkokl@gmail.com
-- Stability : experimental
--
-- Simple linear optimization example, as found in operations research texts.
-----------------------------------------------------------------------------
{-# OPTIONS_GHC -Wall -Werror #-}
module Documentation.SBV.Examples.Optimization.LinearOpt where
import Data.SBV
-- $setup
-- >>> -- For doctest purposes only:
-- >>> import Data.SBV
-- | Taken from <http://people.brunel.ac.uk/~mastjjb/jeb/or/morelp.html>
--
-- * maximize 5x1 + 6x2
-- - subject to
--
-- 1. x1 + x2 <= 10
-- 2. x1 - x2 >= 3
-- 3. 5x1 + 4x2 <= 35
-- 4. x1 >= 0
-- 5. x2 >= 0
--
-- >>> optimize Lexicographic problem
-- Optimal model:
-- x1 = 47 % 9 :: Real
-- x2 = 20 % 9 :: Real
-- goal = 355 % 9 :: Real
problem :: ConstraintSet
problem = do [x1, x2] <- mapM sReal ["x1", "x2"]
constrain $ x1 + x2 .<= 10
constrain $ x1 - x2 .>= 3
constrain $ 5*x1 + 4*x2 .<= 35
constrain $ x1 .>= 0
constrain $ x2 .>= 0
maximize "goal" $ 5 * x1 + 6 * x2
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