The problem of the best selection

Photo by WTFast on Unsplash
In the grim darkness of the future there is only math. Ultramarines army (picture from author’s collection).
P = [ChaosLord, ChaosLordTerminator, DaemonPrinceNurgle, LordContagion, MalignantPlaguecaster, Sorcerer, SorcererTerminator, Typhus, ChaosCultists, PlagueMarines, Poxwalkers,...]
Histogram of the damage for each weapon individually, and the total for 1000 shoots against a standard Space Marine unit.
        Bolter_1 Bolter_2 Bolter_3  Blight_1    Blight_2    Total
count 1000.00 1000.00 1000.00 1000.00 1000.00 1000.00
mean 0.23 0.23 0.21 1.20 1.20 3.08
std 0.46 0.46 0.43 1.46 1.50 2.23
min 0.00 0.00 0.00 0.00 0.00 0.00
25% 0.00 0.00 0.00 0.00 0.00 1.00
50% 0.00 0.00 0.00 1.00 1.00 3.00
75% 0.00 0.00 0.00 2.00 2.00 4.00
max 2.00 2.00 2.00 6.00 6.00 10.00
Objective function:
f(P) = 11*elites_BiologusPutrifier + 25*elites_BlightlordTerminators + 47*elites_DeathshroudTerminator + ... + 4*troops_ChaosCultists + 52*troops_PlagueMarines + troops_Poxwalkers
Death guard with their Primarch Mortarion. (picture from author’s collection)
Restriction: 
hq_ChaosLord + hq_ChaosLordTerminator + hq_DaemonPrinceNurgle + hq_LordContagion + hq_MalignantPlaguecaster + hq_Sorcerer + hq_SorcererTerminator + hq_Typhus >= 1
Restriction
:
hq_ChaosLord + hq_ChaosLordTerminator + hq_DaemonPrinceNurgle + hq_LordContagion + hq_MalignantPlaguecaster + hq_Sorcerer + hq_SorcererTerminator + hq_Typhus <= 2
Restriction: 
175*hq_Typhus + ... + 40*troops_ChaosCultists + 123*troops_PlagueMarines + 60*troops_Poxwalkers <= 1000
elites_Helbrute = 1               # 72 points
fastattack_FoetidBloatDrone = 1 # 99 points
heavysupport_ChaosPredator = 1 # 90 points
heavysupport_Defiler = 1 # 152 points
hq_DaemonPrinceNurgle = 1 # 146 points
hq_Typhus = 1 # 175 points
troops_PlagueMarines = 2 # 123*2 points
Objective = 605
Total cost: 980

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