## Step 1: Define the symbolic representation of the variables
The variables are defined as follows: 
- 'x0' for 'green beans'
- 'x1' for 'peanutbutter sandwiches'
- 'x2' for 'cornichons'
- 'x3' for 'strips of bacon'

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is: $8.3x_0 + 8.2x_1 + 7.13x_2 + 4.73x_3$

## Step 3: List all the constraints in symbolic notation
Constraints:
- $18x_0 + 9x_1 + 5x_2 + 13x_3 \leq 501$ (calcium)
- $22x_0 + 16x_1 + 5x_2 + 22x_3 \leq 251$ (healthiness rating)
- $9x_0 + x_1 + 4x_2 + 2x_3 \leq 180$ (protein)
- $9x_1 + 13x_3 \geq 54$ (calcium from peanutbutter sandwiches and strips of bacon)
- $5x_2 + 13x_3 \geq 102$ (calcium from cornichons and strips of bacon)
- $18x_0 + 13x_3 \geq 70$ (calcium from green beans and strips of bacon)
- $18x_0 + 9x_1 \geq 76$ (calcium from green beans and peanutbutter sandwiches)
- $9x_1 + 5x_2 \geq 96$ (calcium from peanutbutter sandwiches and cornichons)
- $18x_0 + 5x_2 \geq 72$ (calcium from green beans and cornichons)
- $18x_0 + 9x_1 + 5x_2 \geq 125$ (calcium from green beans, peanutbutter sandwiches, and cornichons)
- $9x_1 + 5x_2 + 13x_3 \geq 125$ (calcium from peanutbutter sandwiches, cornichons, and strips of bacon)
- $18x_0 + 5x_2 + 13x_3 \geq 125$ (calcium from green beans, cornichons, and strips of bacon)
- $18x_0 + 9x_1 + 5x_2 + 13x_3 \geq 125$ (calcium from all)
- $18x_0 + 9x_1 + 5x_2 \geq 64$ (calcium from green beans, peanutbutter sandwiches, and cornichons)
- $9x_1 + 5x_2 + 13x_3 \geq 64$ (calcium from peanutbutter sandwiches, cornichons, and strips of bacon)
- $18x_0 + 5x_2 + 13x_3 \geq 64$ (calcium from green beans, cornichons, and strips of bacon)
- $18x_0 + 9x_1 + 5x_2 \geq 90$ (calcium from green beans, peanutbutter sandwiches, and cornichons)
- $9x_1 + 5x_2 + 13x_3 \geq 90$ (calcium from peanutbutter sandwiches, cornichons, and strips of bacon)
- $18x_0 + 5x_2 + 13x_3 \geq 90$ (calcium from green beans, cornichons, and strips of bacon)
- $18x_0 + 9x_1 + 5x_2 + 13x_3 \geq 90$ (calcium from all)
- $22x_0 + 16x_1 \geq 44$ (healthiness rating from green beans and peanutbutter sandwiches)
- $22x_0 + 5x_2 \geq 41$ (healthiness rating from green beans and cornichons)
- $5x_2 + 22x_3 \geq 62$ (healthiness rating from cornichons and strips of bacon)
- $16x_1 + 22x_3 \geq 34$ (healthiness rating from peanutbutter sandwiches and strips of bacon)
- $22x_0 + 16x_1 + 22x_3 \geq 34$ (healthiness rating from green beans, peanutbutter sandwiches, and strips of bacon)
- $22x_0 + 16x_1 + 5x_2 \geq 34$ (healthiness rating from green beans, peanutbutter sandwiches, and cornichons)
- $22x_0 + 16x_1 + 22x_3 \geq 31$ (healthiness rating from green beans, peanutbutter sandwiches, and strips of bacon)
- $22x_0 + 16x_1 + 5x_2 \geq 31$ (healthiness rating from green beans, peanutbutter sandwiches, and cornichons)
- $22x_0 + 16x_1 + 5x_2 + 22x_3 \geq 31$ (healthiness rating from all)
- $x_1 + 2x_3 \geq 26$ (protein from peanutbutter sandwiches and strips of bacon)
- $9x_0 + 4x_2 \geq 29$ (protein from green beans and cornichons)
- $4x_2 + 2x_3 \geq 18$ (protein from cornichons and strips of bacon)
- $9x_0 + x_1 + 4x_2 + 2x_3 \geq 18$ (protein from all)
- $18x_0 + 5x_2 + 13x_3 \leq 250$ (calcium from green beans, cornichons, and strips of bacon)
- $22x_0 + 16x_1 \leq 117$ (healthiness rating from green beans and peanutbutter sandwiches)
- $22x_0 + 5x_2 \leq 219$ (healthiness rating from green beans and cornichons)
- $16x_1 + 22x_3 \leq 181$ (healthiness rating from peanutbutter sandwiches and strips of bacon)
- $22x_0 + 16x_1 + 5x_2 \leq 246$ (healthiness rating from green beans, peanutbutter sandwiches, and cornichons)
- $16x_1 + 5x_2 + 22x_3 \leq 113$ (healthiness rating from peanutbutter sandwiches, cornichons, and strips of bacon)
- $22x_0 + 16x_1 + 22x_3 \leq 224$ (healthiness rating from green beans, peanutbutter sandwiches, and strips of bacon)
- $9x_0 + x_1 \leq 142$ (protein from green beans and peanutbutter sandwiches)
- $9x_0 + 4x_2 \leq 91$ (protein from green beans and cornichons)
- $9x_0 + 2x_3 \leq 112$ (protein from green beans and strips of bacon)

## 4: Write the Gurobi code
```python
import gurobi

# Create a new Gurobi model
m = gurobi.Model()

# Define the variables
x0 = m.addVar(name="green_beans", lb=0)
x1 = m.addVar(name="peanutbutter_sandwiches", lb=0)
x2 = m.addVar(name="cornichons", lb=0)
x3 = m.addVar(name="strips_of_bacon", lb=0)

# Objective function
m.setObjective(8.3 * x0 + 8.2 * x1 + 7.13 * x2 + 4.73 * x3, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(18 * x0 + 9 * x1 + 5 * x2 + 13 * x3 <= 501)
m.addConstr(22 * x0 + 16 * x1 + 5 * x2 + 22 * x3 <= 251)
m.addConstr(9 * x0 + x1 + 4 * x2 + 2 * x3 <= 180)

m.addConstr(9 * x1 + 13 * x3 >= 54)
m.addConstr(5 * x2 + 13 * x3 >= 102)
m.addConstr(18 * x0 + 13 * x3 >= 70)
m.addConstr(18 * x0 + 9 * x1 >= 76)
m.addConstr(9 * x1 + 5 * x2 >= 96)
m.addConstr(18 * x0 + 5 * x2 >= 72)
m.addConstr(18 * x0 + 9 * x1 + 5 * x2 >= 125)
m.addConstr(9 * x1 + 5 * x2 + 13 * x3 >= 125)
m.addConstr(18 * x0 + 5 * x2 + 13 * x3 >= 125)
m.addConstr(18 * x0 + 9 * x1 + 5 * x2 + 13 * x3 >= 125)

m.addConstr(18 * x0 + 9 * x1 + 5 * x2 >= 64)
m.addConstr(9 * x1 + 5 * x2 + 13 * x3 >= 64)
m.addConstr(18 * x0 + 5 * x2 + 13 * x3 >= 64)
m.addConstr(18 * x0 + 9 * x1 + 5 * x2 >= 90)
m.addConstr(9 * x1 + 5 * x2 + 13 * x3 >= 90)
m.addConstr(18 * x0 + 5 * x2 + 13 * x3 >= 90)
m.addConstr(18 * x0 + 9 * x1 + 5 * x2 + 13 * x3 >= 90)

m.addConstr(22 * x0 + 16 * x1 >= 44)
m.addConstr(22 * x0 + 5 * x2 >= 41)
m.addConstr(5 * x2 + 22 * x3 >= 62)
m.addConstr(16 * x1 + 22 * x3 >= 34)
m.addConstr(22 * x0 + 16 * x1 + 22 * x3 >= 34)
m.addConstr(22 * x0 + 16 * x1 + 5 * x2 >= 34)
m.addConstr(22 * x0 + 16 * x1 + 22 * x3 >= 31)
m.addConstr(22 * x0 + 16 * x1 + 5 * x2 >= 31)
m.addConstr(22 * x0 + 16 * x1 + 5 * x2 + 22 * x3 >= 31)

m.addConstr(x1 + 2 * x3 >= 26)
m.addConstr(9 * x0 + 4 * x2 >= 29)
m.addConstr(4 * x2 + 2 * x3 >= 18)
m.addConstr(9 * x0 + x1 + 4 * x2 + 2 * x3 >= 18)

m.addConstr(18 * x0 + 5 * x2 + 13 * x3 <= 250)
m.addConstr(22 * x0 + 16 * x1 <= 117)
m.addConstr(22 * x0 + 5 * x2 <= 219)
m.addConstr(16 * x1 + 22 * x3 <= 181)
m.addConstr(22 * x0 + 16 * x1 + 5 * x2 <= 246)
m.addConstr(16 * x1 + 5 * x2 + 22 * x3 <= 113)
m.addConstr(22 * x0 + 16 * x1 + 22 * x3 <= 224)
m.addConstr(9 * x0 + x1 <= 142)
m.addConstr(9 * x0 + 4 * x2 <= 91)
m.addConstr(9 * x0 + 2 * x3 <= 112)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objval)
    print("Green beans: ", x0.varValue)
    print("Peanutbutter sandwiches: ", x1.varValue)
    print("Cornichons: ", x2.varValue)
    print("Strips of bacon: ", x3.varValue)
else:
    print("No optimal solution found")
```

## 5: Symbolic representation of the problem
```json
{
    'sym_variables': [('x0', 'green beans'), ('x1', 'peanutbutter sandwiches'), ('x2', 'cornichons'), ('x3', 'strips of bacon')],
    'objective_function': '8.3x0 + 8.2x1 + 7.13x2 + 4.73x3',
    'constraints': [
        '18x0 + 9x1 + 5x2 + 13x3 <= 501',
        '22x0 + 16x1 + 5x2 + 22x3 <= 251',
        '9x0 + x1 + 4x2 + 2x3 <= 180',
        '9x1 + 13x3 >= 54',
        '5x2 + 13x3 >= 102',
        '18x0 + 13x3 >= 70',
        '18x0 + 9x1 >= 76',
        '9x1 + 5x2 >= 96',
        '18x0 + 5x2 >= 72',
        '18x0 + 9x1 + 5x2 >= 125',
        '9x1 + 5x2 + 13x3 >= 125',
        '18x0 + 5x2 + 13x3 >= 125',
        '18x0 + 9x1 + 5x2 + 13x3 >= 125',
        '18x0 + 9x1 + 5x2 >= 64',
        '9x1 + 5x2 + 13x3 >= 64',
        '18x0 + 5x2 + 13x3 >= 64',
        '18x0 + 9x1 + 5x2 >= 90',
        '9x1 + 5x2 + 13x3 >= 90',
        '18x0 + 5x2 + 13x3 >= 90',
        '18x0 + 9x1 + 5x2 + 13x3 >= 90',
        '22x0 + 16x1 >= 44',
        '22x0 + 5x2 >= 41',
        '5x2 + 22x3 >= 62',
        '16x1 + 22x3 >= 34',
        '22x0 + 16x1 + 22x3 >= 34',
        '22x0 + 16x1 + 5x2 >= 34',
        '22x0 + 16x1 + 22x3 >= 31',
        '22x0 + 16x1 + 5x2 >= 31',
        '22x0 + 16x1 + 5x2 + 22x3 >= 31',
        'x1 + 2x3 >= 26',
        '9x0 + 4x2 >= 29',
        '4x2 + 2x3 >= 18',
        '9x0 + x1 + 4x2 + 2x3 >= 18',
        '18x0 + 5x2 + 13x3 <= 250',
        '22x0 + 16x1 <= 117',
        '22x0 + 5x2 <= 219',
        '16x1 + 22x3 <= 181',
        '22x0 + 16x1 + 5x2 <= 246',
        '16x1 + 5x2 + 22x3 <= 113',
        '22x0 + 16x1 + 22x3 <= 224',
        '9x0 + x1 <= 142',
        '9x0 + 4x2 <= 91',
        '9x0 + 2x3 <= 112'
    ]
}
```