以下LP代码在哪里出错？

Question

I am trying to solve an LP problem with two variables with two constraints where one is inequality and the other one is equality constraint in Scipy. To convert the inequality in the constraint I have added another variable in it called A .

Min(z) = 80x + 60y

Constraints:

0.2x + 0.32y <= 0.25
x + y = 1
x, y <= 0

I have changed the inequality constraints by the following equations by adding an extra variable A

0.2x + 0.32y + A = 0.25
Min(z) = 80x + 60y + 0A
X+ Y + 0A = 1

from scipy.optimize import linprog
import numpy as np

z = np.array([80, 60, 0])
C = np.array([
[0.2, 0.32, 1],
[1, 1, 0]
])
b = np.array([0.25, 1])
x1 = (0, None)
x2 = (0, None)
sol = linprog(-z, A_eq = C, b_eq = b, bounds = (x1, x2), method='simplex')

However, I am getting an error message

Invalid input for linprog with method = 'simplex'. Length of bounds is inconsistent with the length of c

How can I fix this?

Answer 1

The problem is that you do not provide bounds for A . If you eg run

linprog(-z, A_eq = C, b_eq = b, bounds = (x1, x2, (0, None)), method='simplex')

you will obtain:

     con: array([0., 0.])
     fun: -80.0
 message: 'Optimization terminated successfully.'
     nit: 3
   slack: array([], dtype=float64)
  status: 0
 success: True
       x: array([1.  , 0.  , 0.05])

As you can see, the constraints are met:

0.2 * 1 + 0.32 * 0.0 + 0.05 = 0.25  # (0.2x + 0.32y + A = 0.25)

and also

1 + 0 + 0 = 1  # (X + Y + 0A = 1)