This library implements a simple eDSL for linear programming and a simple wrapper around lp_solve (potentially other solvers can also be plugged in easily). Here's how to solve the farmer example from the lp_solve documentation:
Suppose a farmer has 75 acres on which to plant two crops: wheat and barley. To produce these crops, it costs the farmer (for seed, fertilizer, etc.) $120 per acre for the wheat and $210 per acre for the barley. The farmer has $15000 available for expenses. But after the harvest, the farmer must store the crops while awaiting favourable market conditions. The farmer has storage space for 4000 bushels. Each acre yields an average of 110 bushels of wheat or 30 bushels of barley. If the net profit per bushel of wheat (after all expenses have been subtracted) is $1.30 and for barley is $2.00, how should the farmer plant the 75 acres to maximize profit?
import Control.Monad
import Math.LinProg.LPSolve
import Math.LinProg.Types
data Crop = Wheat | Barley
deriving (Eq, Show, Ord)
lp :: LinProg Double Crop ()
lp = do
let vs@[w, b] = map var [Wheat, Barley]
obj $ negate $ 110 * 1.3 * w + 30 * 2 * b
120 * w + 210 * b <: 15000
110 * w + 30 * b <: 4000
w + b <: 75
main :: IO ()
main = do
sol <- solve lp
print sol
This outputs the solution: Right [(Wheat,21.875),(Barley,53.12499999999999)]. Due to the monadic structure one can build up LPs using the usual monadic controls such as mapM/forM etc, making it quite easy to specify constraints.