Here's the formulation of the linear program and the Gurobi code to solve it:

**Decision Variables:**

*  `x`: Number of chocolate chip cookies baked.
*  `y`: Number of oatmeal cookies baked.

**Objective Function:**

Maximize revenue:  4*x + 3*y

**Constraints:**

* Mixing time: 10x + 20y <= 360
* Vanilla extract: x + 2y <= 50
* Non-negativity: x >= 0, y >= 0


```python
import gurobipy as gp
from gurobipy import GRB

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

# Create variables
x = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="chocolate_chip")
y = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="oatmeal")

# Set objective
m.setObjective(4 * x + 3 * y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(10 * x + 20 * y <= 360, "mixing_time")
m.addConstr(x + 2 * y <= 50, "vanilla")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print(f"Optimal Revenue: ${m.objVal}")
    print(f"Chocolate Chip Cookies: {x.x}")
    print(f"Oatmeal Cookies: {y.x}")
elif m.status == GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print(f"Optimization ended with status {m.status}")

```
