I have the following LP file which is produced by PuLP:

```
\* copynumber *\
Minimize
OBJ: PenaltyTree_48
Subject To
_C1: - A_0 + A_3 - over_0 <= 0
_C10: - B_3 + B_7 + under_9 >= 0
_C11: - D_0 + D_3 - over_10 <= 0
_C12: - D_0 + D_3 + under_11 >= 0
_C13: - N_0 + N_3 - over_12 <= 0
_C14: - N_0 + N_3 + under_13 >= 0
_C15: - N_3 + N_7 - over_14 <= 0
_C16: - N_3 + N_7 + under_15 >= 0
_C17: A_7 - B_7 - over_16 <= 0
_C18: A_7 - B_7 + under_17 >= 0
_C19: - A_7 + N_7 - over_18 <= 0
_C2: - A_0 + A_3 + under_1 >= 0
_C20: - A_7 + N_7 + under_19 >= 0
_C21: C_7 - N_7 - over_20 <= 0
_C22: C_7 - N_7 + under_21 >= 0
_C23: B_7 - C_7 - over_22 <= 0
_C24: B_7 - C_7 + under_23 >= 0
_C25: B_3 - N_3 - over_24 <= 0
_C26: B_3 - N_3 + under_25 >= 0
_C27: A_3 - B_3 - over_26 <= 0
_C28: A_3 - B_3 + under_27 >= 0
_C29: - A_3 + N_3 - over_28 <= 0
_C3: - A_3 + A_7 - over_2 <= 0
_C30: - A_3 + N_3 + under_29 >= 0
_C31: A_0 - N_0 - over_30 <= 0
_C32: A_0 - N_0 + under_31 >= 0
_C33: - A_0 + D_0 - over_32 <= 0
_C34: - A_0 + D_0 + under_33 >= 0
_C35: B_0 - D_0 - over_34 <= 0
_C36: B_0 - D_0 + under_35 >= 0
_C37: - B_0 + N_0 - over_36 <= 0
_C38: - B_0 + N_0 + under_37 >= 0
_C39: D_3 - over_38 <= 1.24660824696
_C4: - A_3 + A_7 + under_3 >= 0
_C40: D_3 + under_39 >= 1.24660824696
_C41: A_7 + B_7 + C_7 + N_7 - over_40 <= 9.80665154278
_C42: A_7 + B_7 + C_7 + N_7 + under_41 >= 9.80665154278
_C43: C_0 - over_42 <= 2.06580795211
_C44: C_0 + under_43 >= 2.06580795211
_C45: A_3 + B_3 + N_3 - over_44 <= 7.1056670077
_C46: A_3 + B_3 + N_3 + under_45 >= 7.1056670077
_C47: A_0 + B_0 + D_0 + N_0 - over_46 <= 7.89518556411
_C48: A_0 + B_0 + D_0 + N_0 + under_47 >= 7.89518556411
_C49: - PenaltyTree_48 + 0.5 over_0 + 0.5 over_10 + 0.5 over_12 + 0.5 over_14
+ 0.02 over_16 + 0.02 over_18 + 0.5 over_2 + 0.02 over_20 + 0.02 over_22
+ 0.02 over_24 + 0.02 over_26 + 0.02 over_28 + 0.02 over_30 + 0.02 over_32
+ 0.02 over_34 + 0.02 over_36 + 4 over_38 + 0.5 over_4 + 4 over_40
+ 4 over_42 + 4 over_44 + 4 over_46 + 0.5 over_6 + 0.5 over_8 + 0.5 under_1
+ 0.5 under_11 + 0.5 under_13 + 0.5 under_15 + 0.02 under_17 + 0.02 under_19
+ 0.02 under_21 + 0.02 under_23 + 0.02 under_25 + 0.02 under_27
+ 0.02 under_29 + 0.5 under_3 + 0.02 under_31 + 0.02 under_33 + 0.02 under_35
+ 0.02 under_37 + 4 under_39 + 4 under_41 + 4 under_43 + 4 under_45
+ 4 under_47 + 0.5 under_5 + 0.5 under_7 + 0.5 under_9 = 0
_C5: - C_0 + C_7 - over_4 <= 0
_C6: - C_0 + C_7 + under_5 >= 0
_C7: - B_0 + B_3 - over_6 <= 0
_C8: - B_0 + B_3 + under_7 >= 0
_C9: - B_3 + B_7 - over_8 <= 0
Bounds
0 <= A_0 <= 4
0 <= A_3 <= 4
0 <= A_7 <= 4
0 <= B_0 <= 4
0 <= B_3 <= 4
0 <= B_7 <= 4
0 <= C_0 <= 4
0 <= C_7 <= 4
0 <= D_0 <= 4
0 <= D_3 <= 4
0 <= N_0 <= 4
0 <= N_3 <= 4
0 <= N_7 <= 4
PenaltyTree_48 free
Generals
A_0
A_3
A_7
B_0
B_3
B_7
C_0
C_7
D_0
D_3
N_0
N_3
N_7
End
```

I manually re-created the code to generate this problem one at a time for testing (see bottom of this post), and found that while PuLP reports the solution to this problem as undefined, CBC itself can produce a optimal solution:

```
>>> p.writeLP("tmp/manual.lp")
>>> status = p.solve(pulp.PULP_CBC_CMD())
>>> print("Solution status: {}".format(pulp.LpStatus[status]))
Solution status: Undefined
```

CBC:

```
Coin:import manual.lp
Coin:solve
<removing intermediate output>
Result - Optimal solution found
Objective value: 3.52498440
```

Why is PuLP not finding the same answer, using the same solver? This problem, visually, seems obvious that it has a optimal solution.

Here is the manual code for producing the LP file:

```
import pulp
p = pulp.LpProblem("copynumber",pulp.LpMinimize)
A_0 = pulp.LpVariable("A_0", lowBound=0, upBound=4, cat="Integer")
A_3 = pulp.LpVariable("A_3", lowBound=0, upBound=4, cat="Integer")
B_0 = pulp.LpVariable("B_0", lowBound=0, upBound=4, cat="Integer")
B_3 = pulp.LpVariable("B_3", lowBound=0, upBound=4, cat="Integer")
B_7 = pulp.LpVariable("B_7", lowBound=0, upBound=4, cat="Integer")
D_0 = pulp.LpVariable("D_0", lowBound=0, upBound=4, cat="Integer")
D_3 = pulp.LpVariable("D_3", lowBound=0, upBound=4, cat="Integer")
N_0 = pulp.LpVariable("N_0", lowBound=0, upBound=4, cat="Integer")
N_3 = pulp.LpVariable("N_3", lowBound=0, upBound=4, cat="Integer")
N_7 = pulp.LpVariable("N_7", lowBound=0, upBound=4, cat="Integer")
A_7 = pulp.LpVariable("A_7", lowBound=0, upBound=4, cat="Integer")
B_7 = pulp.LpVariable("B_7", lowBound=0, upBound=4, cat="Integer")
C_7 = pulp.LpVariable("C_7", lowBound=0, upBound=4, cat="Integer")
C_0 = pulp.LpVariable("C_0", lowBound=0, upBound=4, cat="Integer")
over_0 = pulp.LpVariable("over_0", 0)
under_1 = pulp.LpVariable("under_1", 0)
over_2 = pulp.LpVariable("over_2", 0)
under_3 = pulp.LpVariable("under_3", 0)
over_4 = pulp.LpVariable("over_4", 0)
under_5 = pulp.LpVariable("under_5", 0)
over_6 = pulp.LpVariable("over_6", 0)
under_7 = pulp.LpVariable("under_7", 0)
over_8 = pulp.LpVariable("over_8", 0)
under_9 = pulp.LpVariable("under_9", 0)
over_10 = pulp.LpVariable("over_10", 0)
under_11 = pulp.LpVariable("under_11", 0)
over_12 = pulp.LpVariable("over_12", 0)
under_13 = pulp.LpVariable("under_13", 0)
over_14 = pulp.LpVariable("over_14", 0)
under_15 = pulp.LpVariable("under_15", 0)
over_16 = pulp.LpVariable("over_16", 0)
under_17 = pulp.LpVariable("under_17", 0)
over_18 = pulp.LpVariable("over_18", 0)
under_19 = pulp.LpVariable("under_19", 0)
over_20 = pulp.LpVariable("over_20", 0)
under_21 = pulp.LpVariable("under_21", 0)
over_22 = pulp.LpVariable("over_22", 0)
under_23 = pulp.LpVariable("under_23", 0)
over_24 = pulp.LpVariable("over_24", 0)
under_25 = pulp.LpVariable("under_25", 0)
over_26 = pulp.LpVariable("over_26", 0)
under_27 = pulp.LpVariable("under_27", 0)
over_28 = pulp.LpVariable("over_28", 0)
under_29 = pulp.LpVariable("under_29", 0)
over_30 = pulp.LpVariable("over_30", 0)
under_31 = pulp.LpVariable("under_31", 0)
over_32 = pulp.LpVariable("over_32", 0)
under_33 = pulp.LpVariable("under_33", 0)
over_34 = pulp.LpVariable("over_34", 0)
under_35 = pulp.LpVariable("under_35", 0)
over_36 = pulp.LpVariable("over_36", 0)
under_37 = pulp.LpVariable("under_37", 0)
over_38 = pulp.LpVariable("over_37", 0)
under_39 = pulp.LpVariable("under_39", 0)
over_40 = pulp.LpVariable("over_40", 0)
under_41 = pulp.LpVariable("under_41", 0)
over_42 = pulp.LpVariable("over_42", 0)
under_43 = pulp.LpVariable("under_43", 0)
over_44 = pulp.LpVariable("over_44", 0)
under_45 = pulp.LpVariable("under_45", 0)
over_46 = pulp.LpVariable("over_46", 0)
under_47 = pulp.LpVariable("under_47", 0)
PenaltyTree_48 = pulp.LpVariable("PenaltyTree_48")
p += - A_0 + A_3 - over_0 <= 0
p += - B_3 + B_7 + under_9 >= 0
p += - D_0 + D_3 - over_10 <= 0
p += - D_0 + D_3 + under_11 >= 0
p += - N_0 + N_3 - over_12 <= 0
p += - N_0 + N_3 + under_13 >= 0
p += - N_3 + N_7 - over_14 <= 0
p += - N_3 + N_7 + under_15 >= 0
p += A_7 - B_7 - over_16 <= 0
p += A_7 - B_7 + under_17 >= 0
p += - A_7 + N_7 - over_18 <= 0
p += - A_0 + A_3 + under_1 >= 0
p += - A_7 + N_7 + under_19 >= 0
p += C_7 - N_7 - over_20 <= 0
p += C_7 - N_7 + under_21 >= 0
p += B_7 - C_7 - over_22 <= 0
p += B_7 - C_7 + under_23 >= 0
p += B_3 - N_3 - over_24 <= 0
p += B_3 - N_3 + under_25 >= 0
p += A_3 - B_3 - over_26 <= 0
p += A_3 - B_3 + under_27 >= 0
p += - A_3 + N_3 - over_28 <= 0
p += - A_3 + A_7 - over_2 <= 0
p += - A_3 + N_3 + under_29 >= 0
p += A_0 - N_0 - over_30 <= 0
p += A_0 - N_0 + under_31 >= 0
p += - A_0 + D_0 - over_32 <= 0
p += - A_0 + D_0 + under_33 >= 0
p += B_0 - D_0 - over_34 <= 0
p += B_0 - D_0 + under_35 >= 0
p += - B_0 + N_0 - over_36 <= 0
p += - B_0 + N_0 + under_37 >= 0
p += D_3 - over_38 <= 1.24660824696
p += - A_3 + A_7 + under_3 >= 0
p += D_3 + under_39 >= 1.24660824696
p += A_7 + B_7 + C_7 + N_7 - over_40 <= 9.80665154278
p += A_7 + B_7 + C_7 + N_7 + under_41 >= 9.80665154278
p += C_0 - over_42 <= 2.06580795211
p += C_0 + under_43 >= 2.06580795211
p += A_3 + B_3 + N_3 - over_44 <= 7.1056670077
p += A_3 + B_3 + N_3 + under_45 >= 7.1056670077
p += A_0 + B_0 + D_0 + N_0 - over_46 <= 7.89518556411
p += A_0 + B_0 + D_0 + N_0 + under_47 >= 7.89518556411
p += - C_0 + C_7 - over_4 <= 0
p += - C_0 + C_7 + under_5 >= 0
p += - B_0 + B_3 - over_6 <= 0
p += - B_0 + B_3 + under_7 >= 0
p += - B_3 + B_7 - over_8 <= 0
p += 0.5 * over_0 + 0.5 * over_10 + 0.5 * over_12 + 0.5 * over_14 + 0.02 * over_16 + 0.02 * over_18 + 0.5 * over_2 + 0.02 * over_20 + 0.02 * over_22 + 0.02 * over_24 + 0.02 * over_26 + 0.02 * over_28 + 0.02 * over_30 + 0.02 * over_32 + 0.02 * over_34 + 0.02 * over_36 + 4 * over_38 + 0.5 * over_4 + 4 * over_40 + 4 * over_42 + 4 * over_44 + 4 * over_46 + 0.5 * over_6 + 0.5 * over_8 + 0.5 * under_1 + 0.5 * under_11 + 0.5 * under_13 + 0.5 * under_15 + 0.02 * under_17 + 0.02 * under_19 + 0.02 * under_21 + 0.02 * under_23 + 0.02 * under_25 + 0.02 * under_27 + 0.02 * under_29 + 0.5 * under_3 + 0.02 * under_31 + 0.02 * under_33 + 0.02 * under_35 + 0.02 * under_37 + 4 * under_39 + 4 * under_41 + 4 * under_43 + 4 * under_45 + 4 * under_47 + 0.5 * under_5 + 0.5 * under_7 + 0.5 * under_9 == PenaltyTree_48
p += PenaltyTree_48
p.writeLP("tmp/manual.lp")
```