## 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 stuffed donuts
- $x_2$ as the number of stuffed pastries

The objective is to maximize profit, where the profit per donut is $2 and the profit per pastry is $4. Therefore, the objective function can be represented as:

Maximize: $2x_1 + 4x_2$

The constraints based on the machine availability are:
- Baking machine: $2x_1 + 5x_2 \leq 10000$
- Stuffing machine: $3x_1 + 2x_2 \leq 7000$

Also, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of donuts and pastries cannot be negative.

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'stuffed donuts'), ('x2', 'stuffed pastries')],
    'objective_function': '2*x1 + 4*x2',
    'constraints': [
        '2*x1 + 5*x2 <= 10000',
        '3*x1 + 2*x2 <= 7000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

def solve_bakery_problem():
    # Create a new model
    model = gp.Model("bakery_problem")

    # Define variables
    x1 = model.addVar(name="donuts", lb=0, vtype=gp.GRB.CONTINUOUS)
    x2 = model.addVar(name="pastries", lb=0, vtype=gp.GRB.CONTINUOUS)

    # Objective function: Maximize 2*x1 + 4*x2
    model.setObjective(2*x1 + 4*x2, gp.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(2*x1 + 5*x2 <= 10000, name="baking_machine_constraint")
    model.addConstr(3*x1 + 2*x2 <= 7000, name="stuffing_machine_constraint")

    # Solve the model
    model.optimize()

    # Print the results
    if model.status == gp.GRB.OPTIMAL:
        print(f"Optimal solution: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
        print(f"Max Profit: ${model.objVal:.2f}")
    else:
        print("No optimal solution found.")

solve_bakery_problem()
```