Combinatorial optimization to find the hand of "Millijan"

#Pattern 2
hands = ['Haruka', 'Chihaya', 'Miki', 'true', 'Takane', 'Yayoi', 'Festival', 'true美', 'Emily', 'Ami', 'Momoko', 'Iori', 'Raising']

hand_unit_list = [
 {'member': {'Iori', 'Emily'}, 'name': 'little trip around the world'},
 {'member': {'Emily', 'Festival'}, 'name': 'Charlotte Charlotte'},
 {'member': {'Mami', 'Yayoi'}, 'name': 'Wants →'},
 {'member': {'Chihaya', 'Haruka'}, 'name': 'CRIMSON LOVERS'},
 {'member': {'Miki', 'Iori'}, 'name': "First Don't worry"},
 {'member': {'Raising', 'Iori', 'Momoko'}, 'name': 'Kyun! Vampire girl'},
 {'member': {'true', 'Iori', 'Yayoi'}, 'name': 'Stand-by prince'},
 {'member': {'Miki', 'Iori', 'Takane'}, 'name': '99 Nights'},
 {'member': {'true', 'true美', 'Haruka'}, 'name': 'Don't bloom! !! Maiden Juku'},
 {'member': {'Miki', 'Chihaya', 'Haruka'}, 'name': 'Fate of the World'},
 {'member': {'Mami', 'Ami', 'Yayoi'}, 'name': 'Funny Logic'},
 {'member': {'Miki', 'Mami', 'Ami', 'Iori'}, 'name': 'Hoshisai Stepper'},
 {'member': {'Miki', 'Haruka', 'true', 'Chihaya', 'Yayoi'}, 'name': 'Merry'},
 {'member': {'Miki', 'Haruka', 'true', 'Chihaya', 'Emily'}, 'name': 'World changer'},
 {'member': {'Iori', 'Haruka', 'true', 'true美', 'Ami'}, 'name': 'Miracle Night'},
 {'member': {'Miki', 'Takane', 'true', 'true美', 'Yayoi', 'Ami'}, 'name': 'SHOW at The Live Revolution!'}
]

import pandas as pd
from pulp import lpSum
from ortoolpy import model_max, addbinvars, addvals
df = pd.DataFrame([hand_unit['name'] for hand_unit in hand_unit_list],
                  columns=['name'])
for hand in hands:
    df[hand] = False
for i, hand_unit in enumerate(hand_unit_list):
    for member in hand_unit['member']:
        df.loc[i, member] = True
addbinvars(df)

m = model_max()
m += lpSum(df.Var)
for hand in hands:
    m += lpSum(df[df[hand] == True].Var) <= 1
m.solve()
addvals(df)
print(df[df.Val > 0])

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