CVXPY
Maximize
  Sum(X + Y, None, False)
Subject To
 14: maximum(X, Y) <= 1.0
Bounds
 X free
 Y free
End
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AFTER COMPILATION
Minimize
  - C0 - C1 - C2 - C3 - C4 - C5 - C6 - C7
Subject To
 R0: C0 - C8 <= 0
 R1: C1 - C9 <= 0
 R2: C2 - C10 <= 0
 R3: C3 - C11 <= 0
 R4: C4 - C8 <= 0
 R5: C5 - C9 <= 0
 R6: C6 - C10 <= 0
 R7: C7 - C11 <= 0
 R8: C8 <= 1
 R9: C9 <= 1
 R10: C10 <= 1
 R11: C11 <= 1
Bounds
 C0 free
 C1 free
 C2 free
 C3 free
 C4 free
 C5 free
 C6 free
 C7 free
 C8 free
 C9 free
 C10 free
 C11 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
 14[0,0]: maximum_1 <= 1
 14[0,1]: maximum_2 <= 1
 14[1,0]: maximum_3 <= 1
 14[1,1]: maximum_4 <= 1
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