To solve Amy's bakery optimization problem, we first need to translate the natural language description into a symbolic representation. Let's denote the number of croissants as \(x_1\) and the number of ficelles as \(x_2\).

The objective is to maximize revenue. Each croissant sells for $4.5, and each ficelle sells for $3.5. Thus, the objective function can be represented algebraically as:
\[ \text{Maximize} \quad 4.5x_1 + 3.5x_2 \]

The constraints are based on the available mixing time and vanilla extract:
1. Mixing Time Constraint: Each croissant requires 12 minutes of mixing, and each ficelle requires 17 minutes. There are 350 minutes available.
\[ 12x_1 + 17x_2 \leq 350 \]
2. Vanilla Extract Constraint: Each croissant requires 2 tablespoons of vanilla extract, and each ficelle requires 1 tablespoon. There are 45 tablespoons available.
\[ 2x_1 + x_2 \leq 45 \]

Non-negativity constraints also apply since Amy cannot produce a negative number of bread:
\[ x_1 \geq 0, x_2 \geq 0 \]

Symbolic representation in JSON format:

```json
{
    'sym_variables': [('x1', 'number of croissants'), ('x2', 'number of ficelles')],
    'objective_function': '4.5*x1 + 3.5*x2',
    'constraints': ['12*x1 + 17*x2 <= 350', '2*x1 + x2 <= 45', 'x1 >= 0', 'x2 >= 0']
}
```

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

```python
from gurobipy import *

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

# Create variables
x1 = model.addVar(vtype=GRB.CONTINUOUS, name="croissants")
x2 = model.addVar(vtype=GRB.CONTINUOUS, name="ficelles")

# Set the objective function
model.setObjective(4.5*x1 + 3.5*x2, GRB.MAXIMIZE)

# Add constraints
model.addConstr(12*x1 + 17*x2 <= 350, "mixing_time")
model.addConstr(2*x1 + x2 <= 45, "vanilla_extract")

# Optimize the model
model.optimize()

# Print the results
if model.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Number of croissants: {x1.x}")
    print(f"Number of ficelles: {x2.x}")
    print(f"Maximum revenue: ${4.5*x1.x + 3.5*x2.x:.2f}")
else:
    print("No optimal solution found.")
```