## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are 'potatoes', 'cornichons', and 'peanutbutter sandwiches', which we will denote as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Specify the objective function in symbolic notation
The objective function to maximize is $3x_0 + 2x_1 + 2x_2$.

## 3: List the constraints in symbolic notation
The constraints are:
1. $16x_0 + 24x_1 + 9x_2 \leq 189$ (fiber constraint)
2. $25x_0 + 22x_1 + 2x_2 \leq 193$ (iron constraint)
3. $18x_0 + 18x_1 + 23x_2 \leq 301$ (umami index constraint)
4. $24x_1 + 9x_2 \geq 51$ (fiber from cornichons and peanutbutter sandwiches)
5. $25x_0 + 22x_1 + 2x_2 \geq 51$ (iron from potatoes, cornichons, and peanutbutter sandwiches)
6. $18x_0 + 18x_1 + 23x_2 \geq 90$ (umami index from potatoes, cornichons, and peanutbutter sandwiches)
7. $16x_0 + 9x_2 \leq 66$ (fiber from potatoes and peanutbutter sandwiches)
8. $16x_0 + 24x_1 \leq 91$ (fiber from potatoes and cornichons)
9. $16x_0 + 24x_1 + 9x_2 \leq 91$ (fiber from potatoes, cornichons, and peanutbutter sandwiches)
10. $25x_0 + 2x_2 \leq 168$ (iron from potatoes and peanutbutter sandwiches)
11. $25x_0 + 22x_1 + 2x_2 \leq 168$ (iron from potatoes, cornichons, and peanutbutter sandwiches)
12. $18x_1 + 23x_2 \leq 175$ (umami index from cornichons and peanutbutter sandwiches)
13. $18x_0 + 18x_1 + 23x_2 \leq 175$ (umami index from potatoes, cornichons, and peanutbutter sandwiches)

## 4: Define the symbolic variables
The symbolic variables are:
- $x_0$ for 'potatoes'
- $x_1$ for 'cornichons'
- $x_2$ for 'peanutbutter sandwiches'

## 5: Create the Gurobi model and variables
We will now create a Gurobi model and define the variables.

## 6: Implement the objective function and constraints in Gurobi
```python
import gurobi

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

# Define the variables
x0 = model.addVar(name='potatoes', lb=0)
x1 = model.addVar(name='cornichons', lb=0)
x2 = model.addVar(name='peanutbutter_sandwiches', lb=0)

# Set the objective function
model.setObjective(3*x0 + 2*x1 + 2*x2, gurobi.GRB.MAXIMIZE)

# Add constraints
model.addConstr(16*x0 + 24*x1 + 9*x2 <= 189)  # fiber
model.addConstr(25*x0 + 22*x1 + 2*x2 <= 193)  # iron
model.addConstr(18*x0 + 18*x1 + 23*x2 <= 301)  # umami index
model.addConstr(24*x1 + 9*x2 >= 51)  # fiber from cornichons and peanutbutter sandwiches
model.addConstr(25*x0 + 22*x1 + 2*x2 >= 51)  # iron from potatoes, cornichons, and peanutbutter sandwiches
model.addConstr(18*x0 + 18*x1 + 23*x2 >= 90)  # umami index from potatoes, cornichons, and peanutbutter sandwiches
model.addConstr(16*x0 + 9*x2 <= 66)  # fiber from potatoes and peanutbutter sandwiches
model.addConstr(16*x0 + 24*x1 <= 91)  # fiber from potatoes and cornichons
model.addConstr(16*x0 + 24*x1 + 9*x2 <= 91)  # fiber from potatoes, cornichons, and peanutbutter sandwiches
model.addConstr(25*x0 + 2*x2 <= 168)  # iron from potatoes and peanutbutter sandwiches
model.addConstr(25*x0 + 22*x1 + 2*x2 <= 168)  # iron from potatoes, cornichons, and peanutbutter sandwiches
model.addConstr(18*x1 + 23*x2 <= 175)  # umami index from cornichons and peanutbutter sandwiches
model.addConstr(18*x0 + 18*x1 + 23*x2 <= 175)  # umami index from potatoes, cornichons, and peanutbutter sandwiches

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', model.objVal)
    print('Potatoes: ', x0.x)
    print('Cornichons: ', x1.x)
    print('Peanutbutter sandwiches: ', x2.x)
else:
    print('The model is infeasible')
```

## 7: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'potatoes'), 
        ('x1', 'cornichons'), 
        ('x2', 'peanutbutter sandwiches')
    ], 
    'objective_function': '3*x0 + 2*x1 + 2*x2', 
    'constraints': [
        '16*x0 + 24*x1 + 9*x2 <= 189', 
        '25*x0 + 22*x1 + 2*x2 <= 193', 
        '18*x0 + 18*x1 + 23*x2 <= 301', 
        '24*x1 + 9*x2 >= 51', 
        '25*x0 + 22*x1 + 2*x2 >= 51', 
        '18*x0 + 18*x1 + 23*x2 >= 90', 
        '16*x0 + 9*x2 <= 66', 
        '16*x0 + 24*x1 <= 91', 
        '16*x0 + 24*x1 + 9*x2 <= 91', 
        '25*x0 + 2*x2 <= 168', 
        '25*x0 + 22*x1 + 2*x2 <= 168', 
        '18*x1 + 23*x2 <= 175', 
        '18*x0 + 18*x1 + 23*x2 <= 175'
    ]
}
```