## Symbolic Representation

To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's denote:

- \(x_1\) as the number of small smoothies
- \(x_2\) as the number of large smoothies

The objective is to maximize profit. Given that the profit per small smoothie is $3 and per large smoothie is $5, the objective function can be written as:

\[ \text{Maximize:} \quad 3x_1 + 5x_2 \]

The constraints based on the available ingredients are:

- Each small smoothie requires 2 units of ice cream, and each large smoothie requires 3 units of ice cream. The total available ice cream is 20 units.
- Each small smoothie requires 1 unit of peanut butter, and each large smoothie requires 2 units of peanut butter. The total available peanut butter is 18 units.
- The number of smoothies cannot be negative.

So, the constraints are:

\[ 2x_1 + 3x_2 \leq 20 \]
\[ x_1 + 2x_2 \leq 18 \]
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

And \(x_1, x_2\) should be integers since they represent the number of smoothies.

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'small smoothies'), ('x2', 'large smoothies')],
    'objective_function': '3*x1 + 5*x2',
    'constraints': [
        '2*x1 + 3*x2 <= 20',
        'x1 + 2*x2 <= 18',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="small_smoothies", lb=0, vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="large_smoothies", lb=0, vtype=gurobi.GRB.INTEGER)

    # Objective function: maximize 3*x1 + 5*x2
    model.setObjective(3*x1 + 5*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(2*x1 + 3*x2 <= 20, name="ice_cream_constraint")
    model.addConstr(x1 + 2*x2 <= 18, name="peanut_butter_constraint")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: x1 = {x1.varValue}, x2 = {x2.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("The model is infeasible")

solve_smoothie_problem()
```