I need to build an object.
The object is a mixture of 3 elements.
I need to minimize the object weight, but to keep it robust. (Please pardon my English...)
Elements are noted as in school (x/20), just like in the school class .
The minimum needed object strength is the following note : 10/20 .
strength weight
steel : 18/20 16/20
plastic : 3/20 6/20
ceramic: 12/20 10/20
This is the Pulp Linear Program I have built, what do you think about this, please ?
from pulp import *
# I want to minimize weight
prob = LpProblem("Minimize",LpMinimize)
# Ingredients list and characteristics
products = ["steel", "plastic","ceramic"]
strength = {"steel": 18, "plastic": 3, "ceramic": 12}
weight = {"steel": 16, "plastic": 6, "ceramic": 20}
# Build variables
x = LpVariable.dicts("products ", x , 0)
# Objective function
prob += lpSum([weight[i] * x[i] for i in products ]), "MinimizeWeight"
# Constraints
prob += lpSum([(strength[i] * x[i]) / 20 for i in products]) >= 10, "strength"
# note Max Constraint ( Seen in most of blend problems...)
prob += lpSum([1 * x[f] for f in products]) == 20, "noteMax"
prob.solve()
for v in prob.variables ():
print (v.name, "=", v.varValue)
print ("Note", value (prob.objective /20))
What I can't understand is that constraint should be an average, like this, but it doesn't work :
prob += (lpSum([(strength[i] * x[i]) for i in products]) / 3) >= 10, "strength"
**This is the result I get, is this correct, please ? Basically it says that I should use 9.3/20 steel and 10.6/20 plastic to get the slimmer object as possible but still robust ... Is this right ?
Status: Optimal
products__ceramic = 0.0
products__steel = 9.3333333
products__plastic = 10.666667
Note 10.66666674
question from:
https://stackoverflow.com/questions/65829711/blend-minimize-weight-but-keep-it-robust 
