To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints.

Let's define:
- $x_1$ as the number of bulletproof glass panes produced.
- $x_2$ as the number of fire-rated glass panes produced.

The objective is to maximize profit. Given that the profit per pane of bulletproof glass is $12 and per pane of fire-rated glass is $9.5, the objective function can be represented as:
\[ \text{Maximize} \quad 12x_1 + 9.5x_2 \]

The constraints are based on the time available on the heating and cooling machines. Both machines are available for a maximum of 350 minutes per day.
- It takes 4 minutes in the heating machine to make one bulletproof glass pane, so $x_1$ bulletproof panes will take $4x_1$ minutes.
- It takes 7 minutes in the heating machine to make one fire-rated glass pane, so $x_2$ fire-rated panes will take $7x_2$ minutes.
- The total time used on the heating machine cannot exceed 350 minutes: $4x_1 + 7x_2 \leq 350$.

Similarly, for the cooling machine:
- It takes 6 minutes in the cooling machine to make one bulletproof glass pane, so $x_1$ bulletproof panes will take $6x_1$ minutes.
- It takes 9 minutes in the cooling machine to make one fire-rated glass pane, so $x_2$ fire-rated panes will take $9x_2$ minutes.
- The total time used on the cooling machine cannot exceed 350 minutes: $6x_1 + 9x_2 \leq 350$.

Additionally, the number of panes produced cannot be negative:
\[ x_1 \geq 0, x_2 \geq 0 \]

Symbolic representation:
```json
{
    'sym_variables': [('x1', 'number of bulletproof glass panes'), ('x2', 'number of fire-rated glass panes')],
    'objective_function': '12*x1 + 9.5*x2',
    'constraints': ['4*x1 + 7*x2 <= 350', '6*x1 + 9*x2 <= 350', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this problem in Gurobi using Python:

```python
from gurobipy import *

# Create a new model
model = Model("Glass_Production")

# Create variables
x1 = model.addVar(name='bulletproof_glass_panes', vtype=GRB.CONTINUOUS, lb=0)
x2 = model.addVar(name='fire_rated_glass_panes', vtype=GRB.CONTINUOUS, lb=0)

# Set the objective function
model.setObjective(12*x1 + 9.5*x2, GRB.MAXIMIZE)

# Add constraints
model.addConstr(4*x1 + 7*x2 <= 350, name='heating_machine_time')
model.addConstr(6*x1 + 9*x2 <= 350, name='cooling_machine_time')

# Optimize the model
model.optimize()

# Print the results
if model.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Number of bulletproof glass panes: {x1.x}")
    print(f"Number of fire-rated glass panes: {x2.x}")
    print(f"Maximum profit: ${model.objVal:.2f}")
else:
    print("No optimal solution found.")
```