CVXPY
Maximize
  Sum(X + Y, None, False)
Subject To
 21: maximum(X, Y) <= [[1.00 -2.00]
 [3.00 4.00]]
Bounds
 X free
 Y free
End
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AFTER COMPILATION
Minimize
  - x_0 - x_1 - x_2 - x_3 - x_4 - x_5 - x_6 - x_7
Subject To
 R0: x_0 - x_8 <= 0
 R1: x_1 - x_9 <= 0
 R2: x_2 - x_10 <= 0
 R3: x_3 - x_11 <= 0
 R4: x_4 - x_8 <= 0
 R5: x_5 - x_9 <= 0
 R6: x_6 - x_10 <= 0
 R7: x_7 - x_11 <= 0
 R8: x_8 <= 1
 R9: x_9 <= 3
 R10: x_10 <= -2
 R11: x_11 <= 4
Bounds
 x_0 free
 x_1 free
 x_2 free
 x_3 free
 x_4 free
 x_5 free
 x_6 free
 x_7 free
 x_8 free
 x_9 free
 x_10 free
 x_11 free
End
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GUROBI
Maximize
  X[0,0] + X[0,1] + X[1,0] + X[1,1] + Y[0,0] + Y[0,1] + Y[1,0] + Y[1,1]
Subject To
 21[0,0]: maximum_1 <= 1
 21[0,1]: maximum_2 <= -2
 21[1,0]: maximum_3 <= 3
 21[1,1]: maximum_4 <= 4
Bounds
 X[0,0] free
 X[0,1] free
 X[1,0] free
 X[1,1] free
 Y[0,0] free
 Y[0,1] free
 Y[1,0] free
 Y[1,1] free
 maximum_1 free
 maximum_2 free
 maximum_3 free
 maximum_4 free
General Constraints
 GC0: maximum_1 = MAX ( X[0,0] , Y[0,0] )
 GC1: maximum_2 = MAX ( X[0,1] , Y[0,1] )
 GC2: maximum_3 = MAX ( X[1,0] , Y[1,0] )
 GC3: maximum_4 = MAX ( X[1,1] , Y[1,1] )
End