"""
The Full Whiskas Model Python Formulation for the PuLP Modeller
Authors: Antony Phillips, Dr Stuart Mitchell 2007
"""
# Import PuLP modeler functions
from pulp import *
# Creates a list of the Ingredients
Ingredients = ["CHICKEN", "BEEF", "MUTTON", "RICE", "WHEAT", "GEL"]
# A dictionary of the costs of each of the Ingredients is created
costs = {
"CHICKEN": 0.013,
"BEEF": 0.008,
"MUTTON": 0.010,
"RICE": 0.002,
"WHEAT": 0.005,
"GEL": 0.001,
}
# A dictionary of the protein percent in each of the Ingredients is created
proteinPercent = {
"CHICKEN": 0.100,
"BEEF": 0.200,
"MUTTON": 0.150,
"RICE": 0.000,
"WHEAT": 0.040,
"GEL": 0.000,
}
# A dictionary of the fat percent in each of the Ingredients is created
fatPercent = {
"CHICKEN": 0.080,
"BEEF": 0.100,
"MUTTON": 0.110,
"RICE": 0.010,
"WHEAT": 0.010,
"GEL": 0.000,
}
# A dictionary of the fibre percent in each of the Ingredients is created
fibrePercent = {
"CHICKEN": 0.001,
"BEEF": 0.005,
"MUTTON": 0.003,
"RICE": 0.100,
"WHEAT": 0.150,
"GEL": 0.000,
}
# A dictionary of the salt percent in each of the Ingredients is created
saltPercent = {
"CHICKEN": 0.002,
"BEEF": 0.005,
"MUTTON": 0.007,
"RICE": 0.002,
"WHEAT": 0.008,
"GEL": 0.000,
}
# Create the 'prob' variable to contain the problem data
prob = LpProblem("The Whiskas Problem", LpMinimize)
# A dictionary called 'ingredient_vars' is created to contain the referenced Variables
ingredient_vars = LpVariable.dicts("Ingr", Ingredients, 0)
# The objective function is added to 'prob' first
prob += (
lpSum([costs[i] * ingredient_vars[i] for i in Ingredients]),
"Total Cost of Ingredients per can",
)
# The five constraints are added to 'prob'
prob += lpSum([ingredient_vars[i] for i in Ingredients]) == 100, "PercentagesSum"
prob += (
lpSum([proteinPercent[i] * ingredient_vars[i] for i in Ingredients]) >= 8.0,
"ProteinRequirement",
)
prob += (
lpSum([fatPercent[i] * ingredient_vars[i] for i in Ingredients]) >= 6.0,
"FatRequirement",
)
prob += (
lpSum([fibrePercent[i] * ingredient_vars[i] for i in Ingredients]) <= 2.0,
"FibreRequirement",
)
prob += (
lpSum([saltPercent[i] * ingredient_vars[i] for i in Ingredients]) <= 0.4,
"SaltRequirement",
)
# The problem data is written to an .lp file
prob.writeLP("WhiskasModel2.lp")
# The problem is solved using PuLP's choice of Solver
prob.solve()
# The status of the solution is printed to the screen
print("Status:", LpStatus[prob.status])
# Each of the variables is printed with it's resolved optimum value
for v in prob.variables():
print(v.name, "=", v.varValue)
# The optimised objective function value is printed to the screen
print("Total Cost of Ingredients per can = ", value(prob.objective))