## 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 symbolic variables as follows:

- 'x1' for batches of cupcakes
- 'x2' for batches of cakes

The objective is to maximize profit, with the profit per batch of cupcakes being $10 and per batch of cakes being $25. Therefore, the objective function can be represented as:

Maximize: 10x1 + 25x2

The constraints based on the given resources are:

- Oven time: 20x1 + 60x2 ≤ 9000 (since the oven is available for 9000 minutes per month)
- Cooling rack time: 60x1 + 120x2 ≤ 12000 (since the cooling rack is available for 12000 minutes per month)
- Non-negativity: x1 ≥ 0, x2 ≥ 0 (since the number of batches cannot be negative)

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'batches of cupcakes'), ('x2', 'batches of cakes')],
    'objective_function': '10*x1 + 25*x2',
    'constraints': [
        '20*x1 + 60*x2 <= 9000',
        '60*x1 + 120*x2 <= 12000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define the variables
x1 = model.addVar(name="cupcakes", lb=0)  # batches of cupcakes
x2 = model.addVar(name="cakes", lb=0)     # batches of cakes

# Define the objective function
model.setObjective(10*x1 + 25*x2, gp.GRB.MAXIMIZE)

# Define the constraints
model.addConstr(20*x1 + 60*x2 <= 9000, name="oven_constraint")
model.addConstr(60*x1 + 120*x2 <= 12000, name="cooling_rack_constraint")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Batches of Cupcakes: {x1.varValue}")
    print(f"Batches of Cakes: {x2.varValue}")
    print(f"Max Profit: {model.objVal}")
else:
    print("The model is infeasible or unbounded.")
```