The Simplified Whiskas Model Python Formulation for the PuLP Modeller

import pulp

from pulp import *

prob = LpProblem("The Whiskas Problem",LpMinimize)

LpVariable("example", None, 100)

example

x1=LpVariable("ChickenPercent",0,None,LpInteger)

x2=LpVariable("BeefPercent",0)

prob += 0.013*x1 + 0.008*x2, "Total Cost of Ingredients per can"

prob += x1 + x2 == 100, "PercentagesSum"
prob += 0.100*x1 + 0.200*x2 >= 8.0, "ProteinRequirement"
prob += 0.080*x1 + 0.100*x2 >= 6.0, "FatRequirement"
prob += 0.001*x1 + 0.005*x2 <= 2.0, "FibreRequirement"
prob += 0.002*x1 + 0.005*x2 <= 0.4, "SaltRequirement"

prob.writeLP("WhiskasModel.lp")

prob.solve()

print("Status:", LpStatus[prob.status])

Status: Optimal

for v in prob.variables():
    print(v.name, "=", v.varValue)

BeefPercent = 66.0
ChickenPercent = 34.0

print("Total Cost of Ingredients per can = ", value(prob.objective))

Total Cost of Ingredients per can =  0.97

#The 2 outputs above tell us that chicken makes up 33.33% and Beef makes up 66.67%. The total cost of ingredients per can is 96 cents.

#list of ingredients:
Ingredients = ['CHICKEN', 'BEEF', 'MUTTON', 'RICE', 'WHEAT', 'GEL']

#cost of each of the ingredients:
costs = {'CHICKEN': 0.013, 
         'BEEF': 0.008, 
         'MUTTON': 0.010, 
         'RICE': 0.002, 
         'WHEAT': 0.005, 
         'GEL': 0.001}

#percentage of protein in each of the ingredients:
proteinPercent = {'CHICKEN': 0.100, 
                  'BEEF': 0.200, 
                  'MUTTON': 0.150, 
                  'RICE': 0.000, 
                  'WHEAT': 0.040, 
                  'GEL': 0.000}

#percentage of fat in each of the ingredients:
fatPercent = {'CHICKEN': 0.080, 
              'BEEF': 0.100, 
              'MUTTON': 0.110, 
              'RICE': 0.010, 
              'WHEAT': 0.010, 
              'GEL': 0.000}

#percentage of fiber in each of the ingredients:
fibrePercent = {'CHICKEN': 0.001, 
                'BEEF': 0.005, 
                'MUTTON': 0.003, 
                'RICE': 0.100, 
                'WHEAT': 0.150, 
                'GEL': 0.000}

#percentage of salt in each of the ingredients:
saltPercent = {'CHICKEN': 0.002, 
               'BEEF': 0.005, 
               'MUTTON': 0.007, 
               'RICE': 0.002, 
               'WHEAT': 0.008, 
               'GEL': 0.000}

prob = LpProblem("The Whiskas Problem", LpMinimize)

ingredient_vars = LpVariable.dicts("Ingr",Ingredients,0)

#The objective function of the problem:
prob += lpSum([costs[i]*ingredient_vars[i] for i in Ingredients]), "Total Cost of Ingredients per can"

# The five constraints of the problem:
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, "FiberRequirement"
prob += lpSum([saltPercent[i] * ingredient_vars[i] for i in Ingredients]) <= 0.4, "SaltRequirement"

prob.writeLP("WhiskasModel.lp")

prob.solve()

print("Status:", LpStatus[prob.status])

Status: Optimal

for v in prob.variables():
    print(v.name, "=", v.varValue)

Ingr_BEEF = 60.0
Ingr_CHICKEN = 0.0
Ingr_GEL = 40.0
Ingr_MUTTON = 0.0
Ingr_RICE = 0.0
Ingr_WHEAT = 0.0

print("Total Cost of Ingredients per can = ", value(prob.objective))

Total Cost of Ingredients per can =  0.52

#The 2 outputs above tell us that the optimal solution is 60% Beef and 40% Gel. The total cost of ingredients per can is 52 cents.

The Simplified Whiskas Model Python Formulation for the PuLP Modeller

5/7/2017