Problem with 2 representations of a formulation

Hello, 

I have two representations of the same formulation, but the solution and objective value that I get from solving the two problems are different. This does not quite make sense to me why this is the case. Could you kindly please advise?

Model 1: Bounds of all variables are >= 0

\ LP format - for model browsing. Use MPS format to capture full model detail.
Maximize
  r
Subject To
 R0: 800 y[0] + 650 y[1] + 550 y[2] + 550 y[3] + 650 y[4] + y[5] + y[6]
   + y[7] + y[8] + y[9] + y[10] + y[11] + y[12] + y[13] + y[14] + y[15]
   + y[16] + y[17] + y[18] + y[19] + y[20] + y[21] + y[22] + y[23] + y[24]
   + y[25] + y[26] + y[27] + y[28] + y[29] + y[30] + y[31] + y[32] + y[33]
   + y[34] + y[35] + y[36] + y[37] + y[38] + y[39] + y[40] + y[41] + y[42]
   + y[43] + y[44] + y[45] + y[46] + y[47] + y[48] + y[49] + y[50] + y[51]
   + y[52] + y[53] + y[54] + 16524 z <= 16537
 constraint[0]: r - 40 y[0] - 16 y[1] - 38 y[2] - 8 y[3] - 38 y[4] - y[5]
   - 560 z <= -560
 constraint[1]: - 91 y[0] - 92 y[1] - 39 y[2] - 71 y[3] - 52 y[4] - y[6]
   - 1125 z <= -1125
 constraint[2]: - 10 y[0] - 41 y[1] - 32 y[2] - 30 y[3] - 30 y[4] - y[7]
   - 300 z <= -300
 constraint[3]: - 30 y[0] - 16 y[1] - 71 y[2] - 60 y[3] - 42 y[4] - y[8]
   - 620 z <= -620
 constraint[4]: - 160 y[0] - 150 y[1] - 80 y[2] - 200 y[3] - 170 y[4]
   - y[9] - 2100 z <= -2100
 constraint[5]: - 20 y[0] - 23 y[1] - 26 y[2] - 18 y[3] - 9 y[4] - y[10]
   - 431 z <= -431
 constraint[6]: - 3 y[0] - 4 y[1] - 5 y[2] - 6 y[3] - 7 y[4] - y[11] - 68 z
   <= -68
 constraint[7]: - 12 y[0] - 18 y[1] - 40 y[2] - 30 y[3] - 20 y[4] - y[12]
   - 328 z <= -328
 constraint[8]: - 3 y[0] - 6 y[1] - 8 y[2] - 4 y[3] - y[13] - 47 z <= -47
 constraint[9]: - 18 y[0] - 12 y[2] - 8 y[3] - 3 y[4] - y[14] - 122 z
   <= -122
 constraint[10]: - 9 y[0] - 12 y[1] - 30 y[2] - 31 y[3] - 21 y[4] - y[15]
   - 322 z <= -322
 constraint[11]: - 25 y[0] - 8 y[1] - 15 y[2] - 6 y[3] - 4 y[4] - y[16]
   - 196 z <= -196
 constraint[12]: - y[0] - 2 y[1] - 3 y[3] - y[4] - y[17] - 41 z <= -41
 constraint[13]: - y[0] - y[1] - y[2] - 2 y[4] - y[18] - 25 z <= -25
 constraint[14]: - 10 y[0] - 23 y[2] - 18 y[3] - 14 y[4] - y[19] - 425 z
   <= -425
 constraint[15]: - 280 y[0] - 200 y[1] - 100 y[2] - 60 y[3] - 310 y[4]
   - y[20] - 4260 z <= -4260
 constraint[16]: - 10 y[0] - 20 y[1] - 21 y[3] - 8 y[4] - y[21] - 416 z
   <= -416
 constraint[17]: - 8 y[0] - 6 y[1] - 20 y[2] - 4 y[3] - 4 y[4] - y[22]
   - 115 z <= -115
 constraint[18]: - y[0] - 2 y[1] - 3 y[2] - 6 y[4] - y[23] - 82 z <= -82
 constraint[19]: - y[0] - y[1] - 2 y[3] - y[4] - y[24] - 22 z <= -22
 constraint[20]: - 49 y[0] - 70 y[1] - 40 y[2] - 32 y[3] - 18 y[4] - y[25]
   - 631 z <= -631
 constraint[21]: - 8 y[0] - 9 y[1] - 6 y[2] - 15 y[3] - 15 y[4] - y[26]
   - 132 z <= -132
 constraint[22]: - 21 y[0] - 22 y[1] - 8 y[2] - 31 y[3] - 38 y[4] - y[27]
   - 420 z <= -420
 constraint[23]: - 6 y[0] - 4 y[1] - 2 y[3] - 10 y[4] - y[28] - 86 z
   <= -86
 constraint[24]: - y[0] - y[1] - 6 y[2] - 2 y[3] - 4 y[4] - y[29] - 42 z
   <= -42
 constraint[25]: - 5 y[0] - 5 y[1] - 4 y[2] - 7 y[3] - 8 y[4] - y[30]
   - 103 z <= -103
 constraint[26]: - 10 y[0] - 10 y[1] - 22 y[2] - 8 y[3] - 6 y[4] - y[31]
   - 215 z <= -215
 constraint[27]: - 8 y[0] - 6 y[1] - 4 y[2] - 2 y[3] - y[32] - 81 z <= -81
 constraint[28]: - 2 y[0] - 4 y[1] - 6 y[2] - 8 y[3] - y[33] - 91 z <= -91
 constraint[29]: - y[0] - y[2] - 3 y[4] - y[34] - 26 z <= -26
 constraint[30]: - 4 y[1] - 5 y[2] - 2 y[3] - y[35] - 49 z <= -49
 constraint[31]: - 10 y[0] - 12 y[1] - 14 y[2] - 8 y[3] - 10 y[4] - y[36]
   - 420 z <= -420
 constraint[32]: - 42 y[0] - 8 y[1] - 8 y[2] - 6 y[3] - 6 y[4] - y[37]
   - 316 z <= -316
 constraint[33]: - 6 y[0] - 4 y[1] - 2 y[2] - 7 y[3] - y[4] - y[38] - 72 z
   <= -72
 constraint[34]: - 4 y[0] - 3 y[1] - 8 y[2] - y[3] - 3 y[4] - y[39] - 71 z
   <= -71
 constraint[35]: - 8 y[0] - y[40] - 49 z <= -49
 constraint[36]: - 10 y[1] - 20 y[2] - 3 y[4] - y[41] - 108 z <= -108
 constraint[37]: - 10 y[0] - 20 y[3] - 5 y[4] - y[42] - 116 z <= -116
 constraint[38]: - y[0] - 6 y[1] - 8 y[3] - 4 y[4] - y[43] - 90 z <= -90
 constraint[39]: - 40 y[0] - 28 y[1] - 6 y[2] - 14 y[3] - y[44] - 738 z
   <= -738
 constraint[40]: - 86 y[0] - 93 y[1] - 12 y[2] - 20 y[3] - 30 y[4] - y[45]
   - 1811 z <= -1811
 constraint[41]: - 11 y[0] - 9 y[1] - 6 y[2] - 2 y[3] - 12 y[4] - y[46]
   - 430 z <= -430
 constraint[42]: - 120 y[0] - 30 y[1] - 80 y[2] - 40 y[3] - 16 y[4] - y[47]
   - 3060 z <= -3060
 constraint[43]: - 8 y[0] - 22 y[1] - 13 y[2] - 6 y[3] - 18 y[4] - y[48]
   - 215 z <= -215
 constraint[44]: - 3 y[0] - 6 y[2] - y[3] - 3 y[4] - y[49] - 58 z <= -58
 constraint[45]: - 32 y[0] - 36 y[1] - 22 y[2] - 14 y[3] - 16 y[4] - y[50]
   - 296 z <= -296
 constraint[46]: - 28 y[0] - 45 y[1] - 14 y[2] - 20 y[3] - 22 y[4] - y[51]
   - 620 z <= -620
 constraint[47]: - 13 y[0] - 13 y[1] - 12 y[3] - 30 y[4] - y[52] - 418 z
   <= -418
 constraint[48]: - 2 y[0] - 2 y[1] - y[2] - 4 y[4] - y[53] - 47 z <= -47
 constraint[49]: - 4 y[0] - 2 y[1] - 2 y[2] - y[3] - y[54] - 81 z <= -81
Bounds
End

Model 2: 

\ LP format - for model browsing. Use MPS format to capture full model detail.
Maximize
  r
Subject To
 R0: 800 y[0] + 650 y[1] + 550 y[2] + 550 y[3] + 650 y[4] + y[5] + y[6]
   + y[7] + y[8] + y[9] + y[10] + y[11] + y[12] + y[13] + y[14] + y[15]
   + y[16] + y[17] + y[18] + y[19] + y[20] + y[21] + y[22] + y[23] + y[24]
   + y[25] + y[26] + y[27] + y[28] + y[29] + y[30] + y[31] + y[32] + y[33]
   + y[34] + y[35] + y[36] + y[37] + y[38] + y[39] + y[40] + y[41] + y[42]
   + y[43] + y[44] + y[45] + y[46] + y[47] + y[48] + y[49] + y[50] + y[51]
   + y[52] + y[53] + y[54] + 16524 z[0] + 16524 z[1] + 16524 z[2] <= 16537
 constraint[0]: r - 40 y[0] - 16 y[1] - 38 y[2] - 8 y[3] - 38 y[4] - y[5]
   + 1e+34 z[0] - 573 z[1] - 560 z[2] <= -560
 constraint[1]: - 91 y[0] - 92 y[1] - 39 y[2] - 71 y[3] - 52 y[4] - y[6]
   - 1125 z[0] - 1125 z[1] - 1125 z[2] <= -1125
 constraint[2]: - 10 y[0] - 41 y[1] - 32 y[2] - 30 y[3] - 30 y[4] - y[7]
   - 300 z[0] - 300 z[1] - 300 z[2] <= -300
 constraint[3]: - 30 y[0] - 16 y[1] - 71 y[2] - 60 y[3] - 42 y[4] - y[8]
   - 620 z[0] - 620 z[1] - 620 z[2] <= -620
 constraint[4]: - 160 y[0] - 150 y[1] - 80 y[2] - 200 y[3] - 170 y[4]
   - y[9] - 2100 z[0] - 2100 z[1] - 2100 z[2] <= -2100
 constraint[5]: - 20 y[0] - 23 y[1] - 26 y[2] - 18 y[3] - 9 y[4] - y[10]
   - 431 z[0] - 431 z[1] - 431 z[2] <= -431
 constraint[6]: - 3 y[0] - 4 y[1] - 5 y[2] - 6 y[3] - 7 y[4] - y[11]
   - 68 z[0] - 68 z[1] - 68 z[2] <= -68
 constraint[7]: - 12 y[0] - 18 y[1] - 40 y[2] - 30 y[3] - 20 y[4] - y[12]
   - 328 z[0] - 328 z[1] - 328 z[2] <= -328
 constraint[8]: - 3 y[0] - 6 y[1] - 8 y[2] - 4 y[3] - y[13] - 47 z[0]
   - 47 z[1] - 47 z[2] <= -47
 constraint[9]: - 18 y[0] - 12 y[2] - 8 y[3] - 3 y[4] - y[14] - 122 z[0]
   - 122 z[1] - 122 z[2] <= -122
 constraint[10]: - 9 y[0] - 12 y[1] - 30 y[2] - 31 y[3] - 21 y[4] - y[15]
   - 322 z[0] - 322 z[1] - 322 z[2] <= -322
 constraint[11]: - 25 y[0] - 8 y[1] - 15 y[2] - 6 y[3] - 4 y[4] - y[16]
   - 196 z[0] - 196 z[1] - 196 z[2] <= -196
 constraint[12]: - y[0] - 2 y[1] - 3 y[3] - y[4] - y[17] - 41 z[0]
   - 41 z[1] - 41 z[2] <= -41
 constraint[13]: - y[0] - y[1] - y[2] - 2 y[4] - y[18] - 25 z[0] - 25 z[1]
   - 25 z[2] <= -25
 constraint[14]: - 10 y[0] - 23 y[2] - 18 y[3] - 14 y[4] - y[19] - 425 z[0]
   - 425 z[1] - 425 z[2] <= -425
 constraint[15]: - 280 y[0] - 200 y[1] - 100 y[2] - 60 y[3] - 310 y[4]
   - y[20] - 4260 z[0] - 4260 z[1] - 4260 z[2] <= -4260
 constraint[16]: - 10 y[0] - 20 y[1] - 21 y[3] - 8 y[4] - y[21] - 416 z[0]
   - 416 z[1] - 416 z[2] <= -416
 constraint[17]: - 8 y[0] - 6 y[1] - 20 y[2] - 4 y[3] - 4 y[4] - y[22]
   - 115 z[0] - 115 z[1] - 115 z[2] <= -115
 constraint[18]: - y[0] - 2 y[1] - 3 y[2] - 6 y[4] - y[23] - 82 z[0]
   - 82 z[1] - 82 z[2] <= -82
 constraint[19]: - y[0] - y[1] - 2 y[3] - y[4] - y[24] - 22 z[0] - 22 z[1]
   - 22 z[2] <= -22
 constraint[20]: - 49 y[0] - 70 y[1] - 40 y[2] - 32 y[3] - 18 y[4] - y[25]
   - 631 z[0] - 631 z[1] - 631 z[2] <= -631
 constraint[21]: - 8 y[0] - 9 y[1] - 6 y[2] - 15 y[3] - 15 y[4] - y[26]
   - 132 z[0] - 132 z[1] - 132 z[2] <= -132
 constraint[22]: - 21 y[0] - 22 y[1] - 8 y[2] - 31 y[3] - 38 y[4] - y[27]
   - 420 z[0] - 420 z[1] - 420 z[2] <= -420
 constraint[23]: - 6 y[0] - 4 y[1] - 2 y[3] - 10 y[4] - y[28] - 86 z[0]
   - 86 z[1] - 86 z[2] <= -86
 constraint[24]: - y[0] - y[1] - 6 y[2] - 2 y[3] - 4 y[4] - y[29] - 42 z[0]
   - 42 z[1] - 42 z[2] <= -42
 constraint[25]: - 5 y[0] - 5 y[1] - 4 y[2] - 7 y[3] - 8 y[4] - y[30]
   - 103 z[0] - 103 z[1] - 103 z[2] <= -103
 constraint[26]: - 10 y[0] - 10 y[1] - 22 y[2] - 8 y[3] - 6 y[4] - y[31]
   - 215 z[0] - 215 z[1] - 215 z[2] <= -215
 constraint[27]: - 8 y[0] - 6 y[1] - 4 y[2] - 2 y[3] - y[32] - 81 z[0]
   - 81 z[1] - 81 z[2] <= -81
 constraint[28]: - 2 y[0] - 4 y[1] - 6 y[2] - 8 y[3] - y[33] - 91 z[0]
   - 91 z[1] - 91 z[2] <= -91
 constraint[29]: - y[0] - y[2] - 3 y[4] - y[34] - 26 z[0] - 26 z[1]
   - 26 z[2] <= -26
 constraint[30]: - 4 y[1] - 5 y[2] - 2 y[3] - y[35] - 49 z[0] - 49 z[1]
   - 49 z[2] <= -49
 constraint[31]: - 10 y[0] - 12 y[1] - 14 y[2] - 8 y[3] - 10 y[4] - y[36]
   - 420 z[0] - 420 z[1] - 420 z[2] <= -420
 constraint[32]: - 42 y[0] - 8 y[1] - 8 y[2] - 6 y[3] - 6 y[4] - y[37]
   - 316 z[0] - 316 z[1] - 316 z[2] <= -316
 constraint[33]: - 6 y[0] - 4 y[1] - 2 y[2] - 7 y[3] - y[4] - y[38]
   - 72 z[0] - 72 z[1] - 72 z[2] <= -72
 constraint[34]: - 4 y[0] - 3 y[1] - 8 y[2] - y[3] - 3 y[4] - y[39]
   - 71 z[0] - 71 z[1] - 71 z[2] <= -71
 constraint[35]: - 8 y[0] - y[40] - 49 z[0] - 49 z[1] - 49 z[2] <= -49
 constraint[36]: - 10 y[1] - 20 y[2] - 3 y[4] - y[41] - 108 z[0] - 108 z[1]
   - 108 z[2] <= -108
 constraint[37]: - 10 y[0] - 20 y[3] - 5 y[4] - y[42] - 116 z[0] - 116 z[1]
   - 116 z[2] <= -116
 constraint[38]: - y[0] - 6 y[1] - 8 y[3] - 4 y[4] - y[43] - 90 z[0]
   - 90 z[1] - 90 z[2] <= -90
 constraint[39]: - 40 y[0] - 28 y[1] - 6 y[2] - 14 y[3] - y[44] - 738 z[0]
   - 738 z[1] - 738 z[2] <= -738
 constraint[40]: - 86 y[0] - 93 y[1] - 12 y[2] - 20 y[3] - 30 y[4] - y[45]
   - 1811 z[0] - 1811 z[1] - 1811 z[2] <= -1811
 constraint[41]: - 11 y[0] - 9 y[1] - 6 y[2] - 2 y[3] - 12 y[4] - y[46]
   - 430 z[0] - 430 z[1] - 430 z[2] <= -430
 constraint[42]: - 120 y[0] - 30 y[1] - 80 y[2] - 40 y[3] - 16 y[4] - y[47]
   - 3060 z[0] - 3060 z[1] - 3060 z[2] <= -3060
 constraint[43]: - 8 y[0] - 22 y[1] - 13 y[2] - 6 y[3] - 18 y[4] - y[48]
   - 215 z[0] - 215 z[1] - 215 z[2] <= -215
 constraint[44]: - 3 y[0] - 6 y[2] - y[3] - 3 y[4] - y[49] - 58 z[0]
   - 58 z[1] - 58 z[2] <= -58
 constraint[45]: - 32 y[0] - 36 y[1] - 22 y[2] - 14 y[3] - 16 y[4] - y[50]
   - 296 z[0] - 296 z[1] - 296 z[2] <= -296
 constraint[46]: - 28 y[0] - 45 y[1] - 14 y[2] - 20 y[3] - 22 y[4] - y[51]
   - 620 z[0] - 620 z[1] - 620 z[2] <= -620
 constraint[47]: - 13 y[0] - 13 y[1] - 12 y[3] - 30 y[4] - y[52] - 418 z[0]
   - 418 z[1] - 418 z[2] <= -418
 constraint[48]: - 2 y[0] - 2 y[1] - y[2] - 4 y[4] - y[53] - 47 z[0]
   - 47 z[1] - 47 z[2] <= -47
 constraint[49]: - 4 y[0] - 2 y[1] - 2 y[2] - y[3] - y[54] - 81 z[0]
   - 81 z[1] - 81 z[2] <= -81
 R51: z[0] = 0
 R52: z[1] = 0
Bounds
End

Observe that in the second model, functionally we have z[0] = 0 , z[1] = 0, which makes the only valid z variable as z[2]. We can then drop all z[0], z[1] variables, returning the same model as model 1. 

Unfortunately, even in this instance, I get that the two problems return a solution of 13 for model 1 and 0 for model 2 respectively, which should not be the case.

Is there any reason to why this is so?