Solvable Simultaneous Equations Returns "Infeasible model"

I am trying to solve a set of 10 by 10 simultaneous equations using gurobipy. The original code is shown below:

import gurobipy as gp
import numpy as np

A = np.array(
[[0, 0, -2.25171, -8.95928, -4.4778, 1.21527, 0, 0, 26.39027, 0], 
[27.06379, 14.61077, 0, 0, 27.01525, -0.62793, 0, 0, 0, 16.96571], 
[14.80508, 0.83121, -1.55167, 0, 23.91044, 0, 2.22328, 14.09781, -1.06263, -9.70157],
[3.18459, 0, -1.00949, -1.554, 0, -3.44998, 0, 0, 16.22922, 5.14289],
[13.29879, 0, -8.46611, -7.69697, 0, 0, 9.19035, 2.16896, 8.83559, 0],
[11.80379, 17.47908, 16.50753, 10.99252, 0, 0, 0, 0, 24.69994, -8.05508],
[3.05873, -7.80076, 10.46765, -9.21063, 0, 0, 6.59954, 3.85601, 0, -3.60016],
[0, 0, 25.75262, 18.11505, -3.52464, 5.82234, 11.77743, 21.51821, 0, 0],
[0, 0, 0, 0, 10.14581, -4.08672, -5.20011, 21.21334, 9.89348, 0],
[23.38353, 0, 24.02229, 21.91727, -4.9149, 0, 0, 1.15203, 0, 0.0554]])

b = np.array([[41.50387],[17.7489],[33.95538],[15.73681],[48.93402],[38.87969],[12.6149],
[12.82158],[49.51045],[24.03097]])

b_t = np.reshape(b, -1)

model = gp.Model()
x = model.addMVar(10)
model.addConstr(A@x == b_t)
model.optimize()

print("Result:")

When I am trying to solve for Ax = b_t, the optimizer shows "Infeasible model". But the simultaneous equations are solvable using x = A inverse multiplies by b, which gives the result of:

Please let me know what did I do wrong with the gurobipy model. Thanks!

Official comment

Simranjit Kaur

Gurobi Staff

June 23, 2025 02:44 Edited

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Thomas Opfer

November 22, 2021 11:10

Without having verified this, I guess you are using the default lower bound of 0. You should add the variables with lower bound -INF.

Best regards,
Thomas

Yen-Yu Chen

November 25, 2021 06:25

Hi Thomas,

Thanks for the reply. The problem was indeed caused by me not defining lower bound/upper bound. I added the bounds in the add variable section and now it works!

November 25, 2021 06:54

The default upper bound should be +INF, so you should not have to specify it explicitly. But of course, it is perfectly ok to do so.

Solvable Simultaneous Equations Returns "Infeasible model"

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