Here's the formulation and the Gurobi code:

**Decision Variables:**

* `x`: Number of pitchers of green tea made.
* `y`: Number of batches of pancakes made.

**Objective Function:**

Maximize profit: `2.5x + 10y`

**Constraints:**

* Joy's time constraint: `0.7x + 1.2y <= 8`
* Willa's time constraint: `0.3x + 0.6y <= 5`
* Non-negativity constraints: `x >= 0`, `y >= 0`


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

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

# Create variables
x = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="green_tea") # Pitchers of green tea
y = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="pancakes") # Batches of pancakes

# Set objective function
m.setObjective(2.5 * x + 10 * y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(0.7 * x + 1.2 * y <= 8, "joy_time")
m.addConstr(0.3 * x + 0.6 * y <= 5, "willa_time")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print(f"Optimal profit: ${m.objVal:.2f}")
    print(f"Green tea pitchers: {x.x:.2f}")
    print(f"Pancake batches: {y.x:.2f}")
elif m.status == GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print(f"Optimization ended with status {m.status}")

```
