## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the number of bottles of Alpha.
- $x_2$ represents the number of bottles of Beta.

## Step 2: Translate the objective function into symbolic notation
The objective is to maximize profit. One bottle of Alpha gives a profit of $4, and one bottle of Beta gives a profit of $6. Therefore, the objective function can be written as:
\[ \text{Maximize:} \quad 4x_1 + 6x_2 \]

## 3: Translate the constraints into symbolic notation
1. Total extract used: $15x_1 + 25x_2 \leq 2000$ (since 2000 grams of extract are available).
2. Demand constraint: $x_1 \geq 3x_2$ (at least three times as many Alpha as Beta).
3. Minimum Beta production: $x_2 \geq 10$ (at least 10 bottles of Beta).
4. Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$ (number of bottles cannot be negative).

## 4: List the symbolic representation of the problem
```json
{
    'sym_variables': [('x1', 'Alpha'), ('x2', 'Beta')],
    'objective_function': '4*x1 + 6*x2',
    'constraints': [
        '15*x1 + 25*x2 <= 2000',
        'x1 >= 3*x2',
        'x2 >= 10',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## 5: Convert the problem into Gurobi code
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name='Alpha', lb=0, vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name='Beta', lb=0, vtype=gurobi.GRB.INTEGER)

    # Objective function: Maximize 4*x1 + 6*x2
    model.setObjective(4*x1 + 6*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(15*x1 + 25*x2 <= 2000, name='extract_constraint')
    model.addConstr(x1 >= 3*x2, name='demand_constraint')
    model.addConstr(x2 >= 10, name='min_beta_constraint')

    # Solve the model
    model.optimize()

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

solve_optimization_problem()
```