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Example Problem:

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

maximize Z = 10x0 + 6x1 + 4x2

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

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()