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Example problem:

http://www.cs.cornell.edu/~tomf/pyglpk/ex_ref.html

maximize Z = 10×0 + 6×1 + 4×2

subject to
p = x0 + x1 + x2
q = 10×0 + 4×1 + 5×2
r = 2×0 + 2×1 + 6×2

and bounds of variables
−∞ < p ≤ 100
−∞ < q ≤ 600
−∞ < r ≤ 300
0 ≤ x0 < ∞
0 ≤ x1 < ∞
0 ≤ x2 < ∞

Standard form:
-———————

import glpkwrap

prob = glpkwrap.LinearProblem(“Standard Example”, ‘max’)

x0 = prob.variable(“x0”,0)

x1 = prob.variable(“x1”,0)

x2 = prob.variable(“x2”,0)

prob.constraints = [

   x0 + x1 + x2 <= 100,

   10*x0 + 4*x1 + 5*x2 <= 600,

   2*x0 + 2*x1 + 6*x2 <= 300

]

prob.objective = [10*x0 + 6*x1 + 4*x2]

prob.solve()

prob.print_results()

Goal form:
-———————

import glpkwrap

prob = glpkwrap.LinearProblem(“Goal Exammple”)

x0 = prob.variable(“x0”,0)

x1 = prob.variable(“x1”,0)

x2 = prob.variable(“x2”,0)

n1 = prob.variable(“n1”,0)

n2 = prob.variable(“n2”,0)

n3 = prob.variable(“n3”,0)

n4 = prob.variable(“n4”,0)

p1 = prob.variable(“p1”,0)

p2 = prob.variable(“p2”,0)

p3 = prob.variable(“p3”,0)

p4 = prob.variable(“p4”,0)

f1 = 10*x0 + 6*x1 + 4*x2 + n1 – p1 == 1000

f2 = x0 + x1 + x2 + n2 – p2 == 100

f3 = 10*x0 + 4*x1 + 5*x2 + n3 – p3 == 600

f4 = 2*x0 + 2*x1 + 6*x2 + n4 – p4 == 300

prob.constraints = [f1, f2, f3, f4]

prob.objective = [p2+p3+p4, n1]

prob.solve()

prob.print_results()