Python 纸浆生产LP文件，可通过命令行CBC解决，但纸浆报告未定义的解决方案

我有以下由纸浆公司制作的LP文件：

\* 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

CBC：

Coin:import manual.lp
硬币：解决
结果-找到了最优解
目标值：3.52498440

为什么纸浆没有找到相同的答案，使用相同的解算器？从视觉上看，这个问题显然有一个最佳解决方案

以下是生成LP文件的手动代码：

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")

进口纸浆
p=纸浆.lp问题（“copynumber”，纸浆.lp）
A_0=pill.LpVariable（“A_0”，下限=0，上限=4，cat=“Integer”）
A_3=纸浆.LpVariable（“A_3”，下限=0，上限=4，cat=“Integer”）
B_0=纸浆.LpVariable（“B_0”，下限=0，上限=4，cat=“Integer”）
B_3=纸浆.LpVariable（“B_3”，下限=0，上限=4，cat=“整数”）
B_7=纸浆.LpVariable（“B_7”，下限=0，上限=4，cat=“Integer”）
D_0=纸浆.LpVariable（“D_0”，下限=0，上限=4，cat=“整数”）
D_3=纸浆.LpVariable（“D_3”，下限=0，上限=4，cat=“整数”）
N_0=纸浆.LpVariable（“N_0”，下限=0，上限=4，cat=“整数”）
N_3=纸浆.LpVariable（“N_3”，下限=0，上限=4，cat=“Integer”）
N_7=纸浆.LpVariable（“N_7”，下限=0，上限=4，cat=“Integer”）
A_7=pill.LpVariable（“A_7”，下限=0，上限=4，cat=“Integer”）
B_7=纸浆.LpVariable（“B_7”，下限=0，上限=4，cat=“Integer”）
C_7=纸浆.LpVariable（“C_7”，下限=0，上限=4，cat=“Integer”）
C_0=纸浆.LpVariable（“C_0”，下限=0，上限=4，cat=“Integer”）
over_0=纸浆.LpVariable（“over_0”，0）
under_1=纸浆.LpVariable（“under_1”，0）
over_2=纸浆.LpVariable（“over_2”，0）
under_3=纸浆.LpVariable（“under_3”，0）
over_4=纸浆.LpVariable（“over_4”，0）
under_5=纸浆.LpVariable（“under_5”，0）
over_6=纸浆.LpVariable（“over_6”，0）
under_7=纸浆.LpVariable（“under_7”，0）
over_8=纸浆.LpVariable（“over_8”，0）
under_9=纸浆.LpVariable（“under_9”，0）
over_10=纸浆.LpVariable（“over_10”，0）
under_11=纸浆.LpVariable（“under_11”，0）
over_12=纸浆.LpVariable（“over_12”，0）
under_13=纸浆.LpVariable（“under_13”，0）
over_14=纸浆.LpVariable（“over_14”，0）
under_15=纸浆.LpVariable（“under_15”，0）
over_16=纸浆.LpVariable（“over_16”，0）
under_17=纸浆.LpVariable（“under_17”，0）
over_18=纸浆.LpVariable（“over_18”，0）
under_19=纸浆.LpVariable（“under_19”，0）
over_20=纸浆.LpVariable（“over_20”，0）
under_21=纸浆.LpVariable（“under_21”，0）
over_22=纸浆.LpVariable（“over_22”，0）
under_23=纸浆.LpVariable（“under_23”，0）
over_24=纸浆.LpVariable（“over_24”，0）
under_25=纸浆.LpVariable（“under_25”，0）
over_26=纸浆.LpVariable（“over_26”，0）
under_27=纸浆.LpVariable（“under_27”，0）
over_28=纸浆.LpVariable（“over_28”，0）
under_29=纸浆.LpVariable（“under_29”，0）
over_30=纸浆.LpVariable（“over_30”，0）
under_31=纸浆.LpVariable（“under_31”，0）
over_32=纸浆.LpVariable（“over_32”，0）
under_33=纸浆.LpVariable（“under_33”，0）
over_34=纸浆.LpVariable（“over_34”，0）
under_35=纸浆.LpVariable（“under_35”，0）
over_36=纸浆.LpVariable（“over_36”，0）
under_37=纸浆.LpVariable（“under_37”，0）
over_38=纸浆.LpVariable（“over_37”，0）
under_39=纸浆.LpVariable（“under_39”，0）
over_40=纸浆.LpVariable（“over_40”，0）
under_41=纸浆.LpVariable（“under_41”，0）
over_42=纸浆.LpVariable（“over_42”，0）
under_43=纸浆.LpVariable（“under_43”，0）
over_44=纸浆.LpVariable（“over_44”，0）
under_45=纸浆.LpVariable（“under_45”，0）
over_46=纸浆.LpVariable（“over_46”，0）
under_47=纸浆.LpVariable（“under_47”，0）
PenaltyTree_48=纸浆.LpVariable（“PenaltyTree_48”）
p+=-A_0+A_3-超过0=0
p+=-D_0+D_3-超过10=0
p+=-N_0+N_3-超过_12=0
p+=-N_3+N_7-超过_14=0
p+=A_7-B_7-over_16=0
p+=-A_7+N_7-超过18=0
p+=-A\u 7+N\u 7+在\u 19>下=0
p+=C_7-N_7-over_20=0
p+=B_7-C_7-over_22=0
p+=B_3-N_3-over_24=0
p+=A_3-B_3-over_26=0
p+=-A_3+N_3-超过_28=1.24660824696
p+=A_7+B_7+C_7+N_7-超过_40=9.80665154278
p+=C_0-超过_42=2.06580795211
p+=A_3+B_3+N_3-超过_44=7.1056670077
p+=A_0+B_0+D_0+N_0-超过_46=7.89518556411
p+=-C_0+C_7-over_4=0
p+=-B_0+B_3-超过6=0
p+=-B_3+B_7-超过8这似乎是由于旧版cbc随第1.5.6版纸浆一起装运时出现错误造成的。我将尽快用第1.5.7版纸浆重新包装新版本的cbc。
此外，您还可以使用COIN_CMD解算器使用其他版本的CBC（如果它在路径上）。
这似乎是由于旧版本的CBC随Palm 1.5.6一起提供的错误造成的。我将尽快用Palm 1.5.7重新打包新版本的CBC。
您还可以使用COIN_CMD解算器使用其他版本的CBC（如果它在路径上）

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

Objective value:                3.52498440

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")