Simple Symbolic LP problem to Matrix form

I solved a linear programming problem and here is my symbolic form code.

import cvxpy as cp
import numpy as np

x11 = cp.Variable(nonneg=True)
x12 = cp.Variable(nonneg=True)
x21 = cp.Variable(nonneg=True)
x22 = cp.Variable(nonneg=True)
x31 = cp.Variable(nonneg=True)
x32 = cp.Variable(nonneg=True)

constraints = [x11 + x12 == 1000,
              x21 + x22 == 1500,
              x31 + x32 == 1200,
              x11 + x21 + x31 == 2300,
              x12 + x22 + x32 == 1400]

obj = cp.Minimize((80*x11 + 215*x12 + 100*x21 + 108*x22 + 102*x31 + 68*x32))

prob = cp.Problem(obj, constraints)
prob.solve()
print('status: ', prob.status)
print('optimal value: ', prob.value)
print('optimal variables: ', x11.value, x12.value, x21.value, x22.value, x31.value, x32.value)

status: optimal

optimal value: 313200.00003146095

optimal variables: 999.9999999627637 3.7235625579412695e-08 1299.99999940076 200.00000059923934 6.364774533690845e-07 1199.999999363524

But I want to change this code to matrix form. here is my another code for matrix form

x = cp.Variable((3, 2), nonneg=True)

constraints = [cp.sum(x[0,:]) == 1000,
              cp.sum(x[1,:]) == 1500,
              cp.sum(x[2,:]) == 1200,
              cp.sum(x[:, 0]) == 2300,
              cp.sum(x[:, 1]) == 1400]

coe = [[80, 215], [100, 108], [102, 68]]

t
obj = cp.Minimize(cp.sum(coe @ x))

prob = cp.Problem(obj, constraints)
prob.solve()
print('status: ', prob.status)
print('optimal value: ', prob.value)
for i in range(3):
    for j in range(2):
        print('optimal variables:x('+str(i)+','+str(j)+')', x[i,j].value)

status: optimal

optimal value: 810999.9999986519

optimal variables:x(0,0) 649.9892627159586

optimal variables:x(0,1) 350.01073728291954

optimal variables:x(1,0) 900.0113075911175

optimal variables:x(1,1) 599.9886924056102

optimal variables:x(2,0) 749.9994296884455

optimal variables:x(2,1) 450.00057030957413

I think the results should be same and the matrix form code is wrong. Could you find my mistakes?

Solution

You must be careful when you work on matrix multiplication especially on different libraries. I found that @ is used in matrix-matrix multiplication. And not a element-wise multiplicationin. See cvxpy's official documents.

Somehow during @ multiplication, cvxpy misunderstands your target.

Solution: change obj = cp.Minimize(cp.sum(coe @ x)) to

obj = cp.Minimize(cp.sum(cp.multiply(coe, x.T))) (I'm also confused why coe is regarded as (2x3))