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Project: Stephen Mackes - MAT 345 Advanced Mathematical Modeling

Path: major-project-3/ProjectWork.ipynb

Views: ⁵³

Kernel: SageMath (stable)

Chipotle!!!!!!!!!!!!!!!!!!!!!!!!!

The matrix M has rows for each ingredient and columns for attributes. The ingredients have different sections The attributes of the ingredients are as follows: Taste Rank (1-100), Cost, Calories, Total Fat (G), Sodium (MG), Protein (G), and Sugar (G).

In [187]:

Mfood=["chicken", "steak", "Carnitas", "Barbacoa", "Sofritas", "Veggies with Guac", "White Rice", "Brown Rice", "Black Beans", "Pinto Beans", "Fajita Veggies", "Queso", "Tomato salsa", "Chilicorn salsa", "Tomatillo green", "Tomatillo-red", "Sour cream", "Cheese", "Guacamole", "Lettuce"]

In [188]:

M=[[98,6.85,180,7,310,32,0],[90,7.85,150,6,330,21,0],[40,7.3,210,12,450,23,0],[40,7.85,170,7,530,24,0],[50,6.85,150,10,560,8,5],[60,4.8,40,0,300,2,4],[65,0,210,4,350,4,0],[55,0,210,6,190,4,0],[65,0,130,1.5,210,8,2],[50,0,130,1.5,210,8,1],[7,0,20,0,150,1,2],[80,1.25,120,8,200,6,1],[65,0,25,0,550,0,1],[50,0,80,1.5,330,3,4],[25,0,15,0,260,0,2],[65,0,30,0,500,0,0],[58,0,110,9,30,2,2],[79,0,110,8,190,6,0],[93,2.05,230,22,370,2,1],[50,0,5,0,0,0,0]]
show(matrix(RDF,M))

Out[188]:

In [189]:

costs=[M[i][1] for i in range(20)]
costs

Out[189]:

[6.85000000000000,
 7.85000000000000,
 7.30000000000000,
 7.85000000000000,
 6.85000000000000,
 4.80000000000000,
 0,
 0,
 0,
 0,
 0,
 1.25000000000000,
 0,
 0,
 0,
 0,
 0,
 0,
 2.05000000000000,
 0]

In [190]:

tr=[M[i][0] for i in range(20)] #taste rank
tr

Out[190]:

[98, 90, 40, 40, 50, 60, 65, 55, 65, 50, 7, 80, 65, 50, 25, 65, 58, 79, 93, 50]

In [191]:

# objective for taste rank. We want to maximize 
objtaste=0
for i in range(20):
    objtaste+=M[i][0]*x[i]
objtaste

Out[191]:

98*x_0 + 90*x_1 + 40*x_2 + 40*x_3 + 50*x_4 + 60*x_5 + 65*x_6 + 55*x_7 + 65*x_8 + 50*x_9 + 7*x_10 + 80*x_11 + 65*x_12 + 50*x_13 + 25*x_14 + 65*x_15 + 58*x_16 + 79*x_17 + 93*x_18 + 50*x_19

In [192]:

# objective for cost. We want to minimize
objcost=0
for i in range(20):
    objcost+=M[i][1]*x[i]
objcost

Out[192]:

6.85*x_0 + 7.85*x_1 + 7.3*x_2 + 7.85*x_3 + 6.85*x_4 + 4.8*x_5 + 1.25*x_11 + 2.05*x_18

x[i]=the item that we include in the bowl x[taste rank, cost,calories,fat,sodium,protein, sugar] x[i,j,k,l,m,n,o]

Parameters

In [0]:

In [182]:

p=MixedIntegerLinearProgram(maximization=True)
x=p.new_variable(binary=True)
#Calories constraint min
p.add_constraint(add([x[i]*M[i][2] for i in range(20)]) >= 750)
#Calories constraint max
p.add_constraint(add([x[i]*M[i][2] for i in range(20)]) <= 1000)
#Fat constraint min
p.add_constraint(add([x[i]*M[i][3] for i in range(20)]) >= 15)
#Fat constraint max
p.add_constraint(add([x[i]*M[i][3] for i in range(20)]) <= 32)
#Sodium
p.add_constraint(add([x[i]*M[i][4] for i in range(20)]) <= 940) ##OG sodium constraint was 500. Had to increase for a feasible sol'n
#Protein constraint Min
p.add_constraint(add([x[i]*M[i][5] for i in range(20)]) >= 18)
#Sugar constraint
p.add_constraint(add([x[i]*M[i][6] for i in range(20)]) <= 10)
#Must have 1 meat in the bowl
p.add_constraint(add([x[k] for k in range(6)]) == 1)
p.add_constraint(x[6]+x[7]<=1) #rice constraint
p.add_constraint(x[8]+x[9]<=1) #beans constraint, can only have 1 type max
#when we order veggies, it comes with guac
#p.add_constraint(x[5]+x[18]==0%2)
p.set_objective(objtaste-objcost)
p.show()
p.solve()
soln=p.get_values(x)
soln

Out[182]:

Maximization:
  91.15 x_0 + 82.15 x_1 + 32.7 x_2 + 32.15 x_3 + 43.15 x_4 + 55.2 x_5 + 65.0 x_6 + 55.0 x_7 + 65.0 x_8 + 50.0 x_9 + 7.0 x_10 + 78.75 x_11 + 65.0 x_12 + 50.0 x_13 + 25.0 x_14 + 65.0 x_15 + 58.0 x_16 + 79.0 x_17 + 90.95 x_18 + 50.0 x_19 

Constraints:
  -180.0 x_0 - 150.0 x_1 - 210.0 x_2 - 170.0 x_3 - 150.0 x_4 - 40.0 x_5 - 210.0 x_6 - 210.0 x_7 - 130.0 x_8 - 130.0 x_9 - 20.0 x_10 - 120.0 x_11 - 25.0 x_12 - 80.0 x_13 - 15.0 x_14 - 30.0 x_15 - 110.0 x_16 - 110.0 x_17 - 230.0 x_18 - 5.0 x_19 <= -750.0
  180.0 x_0 + 150.0 x_1 + 210.0 x_2 + 170.0 x_3 + 150.0 x_4 + 40.0 x_5 + 210.0 x_6 + 210.0 x_7 + 130.0 x_8 + 130.0 x_9 + 20.0 x_10 + 120.0 x_11 + 25.0 x_12 + 80.0 x_13 + 15.0 x_14 + 30.0 x_15 + 110.0 x_16 + 110.0 x_17 + 230.0 x_18 + 5.0 x_19 <= 1000.0
  -7.0 x_0 - 6.0 x_1 - 12.0 x_2 - 7.0 x_3 - 10.0 x_4 - 4.0 x_6 - 6.0 x_7 - 1.5 x_8 - 1.5 x_9 - 8.0 x_11 - 1.5 x_13 - 9.0 x_16 - 8.0 x_17 - 22.0 x_18 <= -15.0
  7.0 x_0 + 6.0 x_1 + 12.0 x_2 + 7.0 x_3 + 10.0 x_4 + 4.0 x_6 + 6.0 x_7 + 1.5 x_8 + 1.5 x_9 + 8.0 x_11 + 1.5 x_13 + 9.0 x_16 + 8.0 x_17 + 22.0 x_18 <= 32.0
  310.0 x_0 + 330.0 x_1 + 450.0 x_2 + 530.0 x_3 + 560.0 x_4 + 300.0 x_5 + 350.0 x_6 + 190.0 x_7 + 210.0 x_8 + 210.0 x_9 + 150.0 x_10 + 200.0 x_11 + 550.0 x_12 + 330.0 x_13 + 260.0 x_14 + 500.0 x_15 + 30.0 x_16 + 190.0 x_17 + 370.0 x_18 <= 940.0
  -32.0 x_0 - 21.0 x_1 - 23.0 x_2 - 24.0 x_3 - 8.0 x_4 - 2.0 x_5 - 4.0 x_6 - 4.0 x_7 - 8.0 x_8 - 8.0 x_9 - x_10 - 6.0 x_11 - 3.0 x_13 - 2.0 x_16 - 6.0 x_17 - 2.0 x_18 <= -18.0
  5.0 x_4 + 4.0 x_5 + 2.0 x_8 + x_9 + 2.0 x_10 + x_11 + x_12 + 4.0 x_13 + 2.0 x_14 + 2.0 x_16 + x_18 <= 10.0
  1.0 <= x_0 + x_1 + x_2 + x_3 + x_4 + x_5 <= 1.0
  x_6 + x_7 <= 1.0
  x_8 + x_9 <= 1.0
Variables:
  x_0 is a boolean variable (min=0.0, max=1.0)
  x_1 is a boolean variable (min=0.0, max=1.0)
  x_2 is a boolean variable (min=0.0, max=1.0)
  x_3 is a boolean variable (min=0.0, max=1.0)
  x_4 is a boolean variable (min=0.0, max=1.0)
  x_5 is a boolean variable (min=0.0, max=1.0)
  x_6 is a boolean variable (min=0.0, max=1.0)
  x_7 is a boolean variable (min=0.0, max=1.0)
  x_8 is a boolean variable (min=0.0, max=1.0)
  x_9 is a boolean variable (min=0.0, max=1.0)
  x_10 is a boolean variable (min=0.0, max=1.0)
  x_11 is a boolean variable (min=0.0, max=1.0)
  x_12 is a boolean variable (min=0.0, max=1.0)
  x_13 is a boolean variable (min=0.0, max=1.0)
  x_14 is a boolean variable (min=0.0, max=1.0)
  x_15 is a boolean variable (min=0.0, max=1.0)
  x_16 is a boolean variable (min=0.0, max=1.0)
  x_17 is a boolean variable (min=0.0, max=1.0)
  x_18 is a boolean variable (min=0.0, max=1.0)
  x_19 is a boolean variable (min=0.0, max=1.0)

{0: 1.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
1.0,
1.0,
0.0,
0.0,
1.0,
0.0,
0.0,
0.0,
0.0,
1.0,
0.0,
0.0,
1.0}

In [183]:

for i in range(20):
    if soln[i]==1:
        print(Mfood[i])

Out[183]:

chicken
Brown Rice
Black Beans
Queso
Sour cream
Lettuce

In [184]:

calories=0
for i in range(20):
    if soln[i]==1:
        calories=calories+M[i][2]
calories

Out[184]:

755

In [0]:

In [185]:

M=[["Taste Rank","Cost","Calories","Total Fat","Sodium", "Protein","Sugar"],[98,6.85,180,7,310,32,0],[90,7.85,150,6,330,21,0],[40,7.3,210,12,450,23,0],[40,7.85,170,7,530,24,0],[50,6.85,150,10,560,8,5],[60,4.8,40,0,300,2,4],[65,0,210,4,350,4,0],[55,0,210,6,190,4,0],[65,0,130,1.5,210,8,2],[50,0,130,1.5,210,8,1],[7,0,20,0,150,1,2],[80,1.25,120,8,200,6,1],[65,0,25,0,550,0,1],[50,0,80,1.5,330,3,4],[25,0,15,0,260,0,2],[65,0,30,0,500,0,0],[58,0,110,9,30,2,2],[79,0,110,8,190,6,0],[93,2.05,230,22,370,2,1],[50,0,5,0,0,0,0]]
show(M)
show(matrix(RDF,M))

Out[185]:

WARNING: Some output was deleted.

In [196]:

p=MixedIntegerLinearProgram(maximization=True)
x=p.new_variable(binary=True)
#Calories constraint min
p.add_constraint(add([x[i]*M[i][2] for i in range(20)]) >= 750)
#Calories constraint max
p.add_constraint(add([x[i]*M[i][2] for i in range(20)]) <= 1000)
#Fat constraint min
p.add_constraint(add([x[i]*M[i][3] for i in range(20)]) >= 15)
#Fat constraint max
p.add_constraint(add([x[i]*M[i][3] for i in range(20)]) <= 32)
#Sodium
p.add_constraint(add([x[i]*M[i][4] for i in range(20)]) <= 1300) ##OG sodium constraint was 500. Had to increase for a feasible sol'n
#Protein constraint Min
p.add_constraint(add([x[i]*M[i][5] for i in range(20)]) >= 18)
#Sugar constraint
p.add_constraint(add([x[i]*M[i][6] for i in range(20)]) <= 10)
#Must have 1 meat in the bowl
p.add_constraint(add([x[k] for k in range(6)]) == 1)
p.add_constraint(x[6]+x[7]<=1) #rice constraint
p.add_constraint(x[8]+x[9]<=1) #beans constraint, can only have 1 type max
p.add_constraint(add([x[i] for i in range(12,15)])>=1)
#when we order veggies, it comes with guac
#p.add_constraint(x[5]+x[18]==0%2)
p.set_objective(objtaste-objcost)
p.show()
p.solve()
soln=p.get_values(x)
soln

Out[196]:

Maximization:
  91.15 x_0 + 82.15 x_1 + 32.7 x_2 + 32.15 x_3 + 43.15 x_4 + 55.2 x_5 + 65.0 x_6 + 55.0 x_7 + 65.0 x_8 + 50.0 x_9 + 7.0 x_10 + 78.75 x_11 + 65.0 x_12 + 50.0 x_13 + 25.0 x_14 + 65.0 x_15 + 58.0 x_16 + 79.0 x_17 + 90.95 x_18 + 50.0 x_19 

Constraints:
  -180.0 x_0 - 150.0 x_1 - 210.0 x_2 - 170.0 x_3 - 150.0 x_4 - 40.0 x_5 - 210.0 x_6 - 210.0 x_7 - 130.0 x_8 - 130.0 x_9 - 20.0 x_10 - 120.0 x_11 - 25.0 x_12 - 80.0 x_13 - 15.0 x_14 - 30.0 x_15 - 110.0 x_16 - 110.0 x_17 - 230.0 x_18 - 5.0 x_19 <= -750.0
  180.0 x_0 + 150.0 x_1 + 210.0 x_2 + 170.0 x_3 + 150.0 x_4 + 40.0 x_5 + 210.0 x_6 + 210.0 x_7 + 130.0 x_8 + 130.0 x_9 + 20.0 x_10 + 120.0 x_11 + 25.0 x_12 + 80.0 x_13 + 15.0 x_14 + 30.0 x_15 + 110.0 x_16 + 110.0 x_17 + 230.0 x_18 + 5.0 x_19 <= 1000.0
  -7.0 x_0 - 6.0 x_1 - 12.0 x_2 - 7.0 x_3 - 10.0 x_4 - 4.0 x_6 - 6.0 x_7 - 1.5 x_8 - 1.5 x_9 - 8.0 x_11 - 1.5 x_13 - 9.0 x_16 - 8.0 x_17 - 22.0 x_18 <= -15.0
  7.0 x_0 + 6.0 x_1 + 12.0 x_2 + 7.0 x_3 + 10.0 x_4 + 4.0 x_6 + 6.0 x_7 + 1.5 x_8 + 1.5 x_9 + 8.0 x_11 + 1.5 x_13 + 9.0 x_16 + 8.0 x_17 + 22.0 x_18 <= 32.0
  310.0 x_0 + 330.0 x_1 + 450.0 x_2 + 530.0 x_3 + 560.0 x_4 + 300.0 x_5 + 350.0 x_6 + 190.0 x_7 + 210.0 x_8 + 210.0 x_9 + 150.0 x_10 + 200.0 x_11 + 550.0 x_12 + 330.0 x_13 + 260.0 x_14 + 500.0 x_15 + 30.0 x_16 + 190.0 x_17 + 370.0 x_18 <= 1300.0
  -32.0 x_0 - 21.0 x_1 - 23.0 x_2 - 24.0 x_3 - 8.0 x_4 - 2.0 x_5 - 4.0 x_6 - 4.0 x_7 - 8.0 x_8 - 8.0 x_9 - x_10 - 6.0 x_11 - 3.0 x_13 - 2.0 x_16 - 6.0 x_17 - 2.0 x_18 <= -18.0
  5.0 x_4 + 4.0 x_5 + 2.0 x_8 + x_9 + 2.0 x_10 + x_11 + x_12 + 4.0 x_13 + 2.0 x_14 + 2.0 x_16 + x_18 <= 10.0
  1.0 <= x_0 + x_1 + x_2 + x_3 + x_4 + x_5 <= 1.0
  x_6 + x_7 <= 1.0
  x_8 + x_9 <= 1.0
  - x_12 - x_13 - x_14 <= -1.0
Variables:
  x_0 is a boolean variable (min=0.0, max=1.0)
  x_1 is a boolean variable (min=0.0, max=1.0)
  x_2 is a boolean variable (min=0.0, max=1.0)
  x_3 is a boolean variable (min=0.0, max=1.0)
  x_4 is a boolean variable (min=0.0, max=1.0)
  x_5 is a boolean variable (min=0.0, max=1.0)
  x_6 is a boolean variable (min=0.0, max=1.0)
  x_7 is a boolean variable (min=0.0, max=1.0)
  x_8 is a boolean variable (min=0.0, max=1.0)
  x_9 is a boolean variable (min=0.0, max=1.0)
  x_10 is a boolean variable (min=0.0, max=1.0)
  x_11 is a boolean variable (min=0.0, max=1.0)
  x_12 is a boolean variable (min=0.0, max=1.0)
  x_13 is a boolean variable (min=0.0, max=1.0)
  x_14 is a boolean variable (min=0.0, max=1.0)
  x_15 is a boolean variable (min=0.0, max=1.0)
  x_16 is a boolean variable (min=0.0, max=1.0)
  x_17 is a boolean variable (min=0.0, max=1.0)
  x_18 is a boolean variable (min=0.0, max=1.0)
  x_19 is a boolean variable (min=0.0, max=1.0)

{0: 0.0,
1.0,
0.0,
0.0,
0.0,
0.0,
0.0,
1.0,
1.0,
0.0,
0.0,
0.0,
0.0,
1.0,
0.0,
0.0,
1.0,
1.0,
0.0,
1.0}

In [197]:

for i in range(20):
    if soln[i]==1:
        print(Mfood[i])

Out[197]:

steak
Brown Rice
Black Beans
Chilicorn salsa
Sour cream
Cheese
Lettuce

In [198]:

calories=0
for i in range(20):
    if soln[i]==1:
        calories=calories+M[i][2]
calories

Out[198]:

795

In [0]:

Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more,
all in one place. Commercial Alternative to JupyterHub.

Chipotle!!!!!!!!!!!!!!!!!!!!!!!!!

Parameters

Product

Resources

Company

Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more, all in one place. Commercial Alternative to JupyterHub.

Chipotle!!!!!!!!!!!!!!!!!!!!!!!!!

Parameters

Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more,
all in one place. Commercial Alternative to JupyterHub.