## Symbolic Representation

To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's define the variables and the objective function, as well as the constraints.

- **Variables:**
  - $x_1$ = batches of pancakes
  - $x_2$ = batches of bagels

- **Objective Function:** The profit per batch of pancakes is $25, and the profit per batch of bagels is $30. Therefore, the objective function to maximize profit is:
  - Maximize $25x_1 + 30x_2$

- **Constraints:**
  - Daniel's time constraint: $25x_1 + 9x_2 \leq 150$
  - David's time constraint: $15x_1 + 20x_2 \leq 350$
  - Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
  'sym_variables': [('x1', 'batches of pancakes'), ('x2', 'batches of bagels')],
  'objective_function': '25*x1 + 30*x2',
  'constraints': [
    '25*x1 + 9*x2 <= 150',
    '15*x1 + 20*x2 <= 350',
    'x1 >= 0',
    'x2 >= 0'
  ]
}
```

## Gurobi Code in Python

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="pancakes", lb=0, vtype=gurobi.GRB.INTEGER)  # batches of pancakes
    x2 = model.addVar(name="bagels", lb=0, vtype=gurobi.GRB.INTEGER)  # batches of bagels

    # Objective function: Maximize profit
    model.setObjective(25 * x1 + 30 * x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(25 * x1 + 9 * x2 <= 150, name="daniel_time")
    model.addConstr(15 * x1 + 20 * x2 <= 350, name="david_time")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal batches of pancakes: {x1.varValue}")
        print(f"Optimal batches of bagels: {x2.varValue}")
        print(f"Max Profit: ${model.objVal:.2f}")
    else:
        print("No optimal solution found.")

solve_bakery_problem()
```