Linear programming with scipy.optimize.linprog

Question

I've just check the simple linear programming problem with scipy.optimize.linprog:

1*x[1] + 2x[2] -> max

1*x[1] + 0*x[2] <= 5
0*x[1] + 1*x[2] <= 5
1*x[1] + 0*x[2] >= 1
0*x[1] + 1*x[2] >= 1
1*x[1] + 1*x[2] <= 6

And got the very strange result, I expected that x[1] will be 1 and x[2] will be 5, but:

>>> print optimize.linprog([1, 2], A_ub=[[1, 1]], b_ub=[6], bounds=(1, 5), method='simplex')
  status: 0
   slack: array([ 4.,  4.,  4.,  0.,  0.])
 success: True
     fun: 3.0
       x: array([ 1.,  1.])
 message: 'Optimization terminated successfully.'
     nit: 2

Can anyone explain, why I got this strange result?

Answer 1

optimize.linprog always minimizes your target function. If you want to maximize instead, you can use that max(f(x)) == -min(-f(x))

from scipy import optimize

optimize.linprog(
    c = [-1, -2], 
    A_ub=[[1, 1]], 
    b_ub=[6],
    bounds=(1, 5),
    method='simplex'
)

This will give you your expected result, with the value -f(x) = -11.0

 slack: array([ 0.,  4.,  0.,  4.,  0.])
 message: 'Optimization terminated successfully.'
     nit: 3
       x: array([ 1.,  5.])
  status: 0
 success: True
     fun: -11.0