## Step 1: Define the symbolic representation of the variables
The variables are 'peanutbutter sandwiches', 'lemons', and 'slices of pizza', which we will denote as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $3x_1x_2 + 4x_3^2 + x_2$.

## 3: List the constraints with their symbolic representation
The constraints are:
- $1.84x_1 + 12.6x_3 \geq 32$
- $4.98x_2 + 12.6x_3 \geq 20$
- $1.84x_1 + 4.98x_2 \geq 18$
- $1.84x_1 + 4.98x_2 + 12.6x_3 \geq 18$
- $3.49x_1 + 7.75x_3 \geq 35$
- $3.39x_2 + 7.75x_3 \geq 40$
- $3.49x_1 + 3.39x_2 + 7.75x_3 \geq 26$
- $3.49x_1 + 3.39x_2 + 7.75x_3 \geq 26$
- $6x_1 - 10x_3 \geq 0$
- $9x_2 - 7x_3 \geq 0$
- $3.39^2x_2^2 + 7.75^2x_3^2 \leq 95$
- $3.49x_1 + 3.39x_2 \leq 63$

## 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [('x1', 'peanutbutter sandwiches'), ('x2', 'lemons'), ('x3', 'slices of pizza')],
    'objective_function': '3*x1*x2 + 4*x3^2 + x2',
    'constraints': [
        '1.84*x1 + 12.6*x3 >= 32',
        '4.98*x2 + 12.6*x3 >= 20',
        '1.84*x1 + 4.98*x2 >= 18',
        '1.84*x1 + 4.98*x2 + 12.6*x3 >= 18',
        '3.49*x1 + 7.75*x3 >= 35',
        '3.39*x2 + 7.75*x3 >= 40',
        '3.49*x1 + 3.39*x2 + 7.75*x3 >= 26',
        '3.49*x1 + 3.39*x2 + 7.75*x3 >= 26',
        '6*x1 - 10*x3 >= 0',
        '9*x2 - 7*x3 >= 0',
        '3.39^2*x2^2 + 7.75^2*x3^2 <= 95',
        '3.49*x1 + 3.39*x2 <= 63'
    ]
}
```

## Step 5: Write the Gurobi code for the optimization problem
```python
import gurobi

def optimize_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="peanutbutter_sandwiches", lb=-gurobi.GRB.INFINITY)
    x2 = model.addVar(name="lemons", lb=-gurobi.GRB.INFINITY)
    x3 = model.addVar(name="slices_of_pizza", lb=-gurobi.GRB.INFINITY)

    # Define the objective function
    model.setObjective(3*x1*x2 + 4*x3**2 + x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(1.84*x1 + 12.6*x3 >= 32)
    model.addConstr(4.98*x2 + 12.6*x3 >= 20)
    model.addConstr(1.84*x1 + 4.98*x2 >= 18)
    model.addConstr(1.84*x1 + 4.98*x2 + 12.6*x3 >= 18)
    model.addConstr(3.49*x1 + 7.75*x3 >= 35)
    model.addConstr(3.39*x2 + 7.75*x3 >= 40)
    model.addConstr(3.49*x1 + 3.39*x2 + 7.75*x3 >= 26)
    # Duplicate constraint, remove if intended
    # model.addConstr(3.49*x1 + 3.39*x2 + 7.75*x3 >= 26)
    model.addConstr(6*x1 - 10*x3 >= 0)
    model.addConstr(9*x2 - 7*x3 >= 0)
    model.addConstr(3.39**2*x2**2 + 7.75**2*x3**2 <= 95)
    model.addConstr(3.49*x1 + 3.39*x2 <= 63)

    # Update model
    model.update()

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Peanutbutter sandwiches: ", x1.x)
        print("Lemons: ", x2.x)
        print("Slices of pizza: ", x3.x)
    else:
        print("The model is infeasible")

optimize_problem()
```