## Symbolic Representation

To solve the given 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 chocolate chip cookies
- $x_2$: batches of oatmeal cookies

### Objective Function
The objective is to maximize profit. Given that the profit per batch of chocolate chip cookies is $12 and per batch of oatmeal cookies is $15, the objective function can be represented as:
\[ \text{Maximize:} \quad 12x_1 + 15x_2 \]

### Constraints
1. Gathering ingredients: $10x_1 + 8x_2 \leq 1000$
2. Mixing: $20x_1 + 15x_2 \leq 1200$
3. Baking: $50x_1 + 30x_2 \leq 3000$
4. Non-negativity: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'batches of chocolate chip cookies'), ('x2', 'batches of oatmeal cookies')],
    'objective_function': '12*x1 + 15*x2',
    'constraints': [
        '10*x1 + 8*x2 <= 1000',
        '20*x1 + 15*x2 <= 1200',
        '50*x1 + 30*x2 <= 3000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Cookie Production")

# Define variables
x1 = model.addVar(name="chocolate_chip", lb=0, vtype=gp.GRB.INTEGER)  # batches of chocolate chip cookies
x2 = model.addVar(name="oatmeal", lb=0, vtype=gp.GRB.INTEGER)  # batches of oatmeal cookies

# Objective function: Maximize profit
model.setObjective(12 * x1 + 15 * x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(10 * x1 + 8 * x2 <= 1000, name="gathering_ingredients")
model.addConstr(20 * x1 + 15 * x2 <= 1200, name="mixing")
model.addConstr(50 * x1 + 30 * x2 <= 3000, name="baking")

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal batches of chocolate chip cookies: {x1.varValue}")
    print(f"Optimal batches of oatmeal cookies: {x2.varValue}")
    print(f"Maximal profit: ${model.objVal}")
else:
    print("The model is infeasible.")
```