To solve Linda's bakery problem using linear programming, we first need to define the decision variables and the constraints based on the given information. Let's denote:

- \(x_1\) as the number of chocolate chip cookies produced.
- \(x_2\) as the number of oatmeal cookies produced.

The objective is to maximize revenue. Each chocolate chip cookie sells for $4, and each oatmeal cookie sells for $3. Thus, the objective function can be written as:

\[ \text{Maximize} \quad 4x_1 + 3x_2 \]

Now, let's consider the constraints:

1. **Mixing Time Constraint**: Each chocolate chip cookie requires 10 minutes of mixing, and each oatmeal cookie requires 20 minutes of mixing. There are 360 minutes available.

\[ 10x_1 + 20x_2 \leq 360 \]

2. **Vanilla Extract Constraint**: Each chocolate chip cookie requires 1 tablespoon of vanilla extract, and each oatmeal cookie requires 2 tablespoons. There are 50 tablespoons available.

\[ x_1 + 2x_2 \leq 50 \]

3. **Non-Negativity Constraints**: The number of cookies cannot be negative.

\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

To solve this problem using Gurobi in Python, we'll first need to ensure that the Gurobi library is installed. If not, you can install it via pip:

```bash
pip install gurobipy
```

Here's how you can formulate and solve Linda's bakery problem using Gurobi in Python:

```python
from gurobipy import *

# Create a new model
m = Model("Bakery_Problem")

# Define the decision variables
x1 = m.addVar(lb=0, name="chocolate_chip_cookies")
x2 = m.addVar(lb=0, name="oatmeal_cookies")

# Define the objective function: Maximize revenue
m.setObjective(4*x1 + 3*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(10*x1 + 20*x2 <= 360, name="mixing_time_constraint")
m.addConstr(x1 + 2*x2 <= 50, name="vanilla_extract_constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of chocolate chip cookies: {x1.x}")
    print(f"Number of oatmeal cookies: {x2.x}")
    print(f"Maximum revenue: ${4*x1.x + 3*x2.x:.2f}")
else:
    print("No optimal solution found.")
```

This code defines the model, adds the decision variables and constraints based on the problem description, optimizes the model to maximize revenue, and then prints out the number of each type of cookie that should be produced along with the maximum achievable revenue.