I am trying to solve a simple simplex tableau using the python library scipy.
c = [7, 9, 18, 17] A = [ [2, 4, 5, 7], [ 1, 1, 2, 2], [ 1, 2, 3, 3] ] b = [42, 17, 24] from scipy.optimize import linprog print(linprog(c, A, b, method='simplex')) According to this course from the University Le Havre where this example tableau was used to introduce the simplex method, I should be getting [3,0,7,0] for the variables and 147 for the minimized function.
Instead, I get [0,0,0,0] and 0.
The optimisation sense of your problem setup is incorrect. linprog assumes minimisation but the textbook asks for maximization. Invert the sign of c and the problem succeeds:
import numpy as np from scipy.optimize import linprog c = -np.array((7, 9, 18, 17)) A = [ [2, 4, 5, 7], [1, 1, 2, 2], [1, 2, 3, 3] ] b = [42, 17, 24] result = linprog(c=c, A_ub=A, b_ub=b, method='highs') print(result) message: Optimization terminated successfully. (HiGHS Status 7: Optimal) success: True status: 0 fun: -147.00000000000006 x: [ 3.000e+00 0.000e+00 7.000e+00 0.000e+00] nit: 4 lower: residual: [ 3.000e+00 0.000e+00 7.000e+00 0.000e+00] marginals: [ 0.000e+00 2.000e+00 0.000e+00 1.000e+00] upper: residual: [ inf inf inf inf] marginals: [ 0.000e+00 0.000e+00 0.000e+00 0.000e+00] eqlin: residual: [] marginals: [] ineqlin: residual: [ 1.000e+00 0.000e+00 0.000e+00] marginals: [-0.000e+00 -3.000e+00 -4.000e+00] mip_node_count: 0 mip_dual_bound: 0.0 mip_gap: 0.0 