## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the number of pitchers of green tea.
- $x_2$ represents the number of batches of pancakes.

## Step 2: Formulate the objective function
The profit per pitcher of green tea is $2.5, and the profit per batch of pancakes is $10. The objective function to maximize profit is:
\[ \text{Maximize:} \quad 2.5x_1 + 10x_2 \]

## 3: Define the constraints
- A pitcher of green tea takes 0.7 hours of Joy's time, and a batch of pancakes takes 1.2 hours of Joy's time. Joy has 8 hours available each day.
\[ 0.7x_1 + 1.2x_2 \leq 8 \]
- A pitcher of green tea takes 0.3 hours of Willa's time, and a batch of pancakes takes 0.6 hours of Willa's time. Willa has 5 hours available each day.
\[ 0.3x_1 + 0.6x_2 \leq 5 \]
- The number of pitchers of green tea and batches of pancakes cannot be negative.
\[ x_1 \geq 0, \quad x_2 \geq 0 \]

## 4: Symbolic representation of the problem
The symbolic representation is:
```json
{
    'sym_variables': [('x1', 'pitchers of green tea'), ('x2', 'batches of pancakes')],
    'objective_function': '2.5*x1 + 10*x2',
    'constraints': [
        '0.7*x1 + 1.2*x2 <= 8',
        '0.3*x1 + 0.6*x2 <= 5',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## 5: Gurobi code
Now, let's implement this problem using Gurobi in Python:
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(lb=0, name="green_tea_pitchers")
    x2 = model.addVar(lb=0, name="pancake_batches")

    # Define the objective function
    model.setObjective(2.5 * x1 + 10 * x2, gurobi.GRB.MAXIMIZE)

    # Define the constraints
    model.addConstr(0.7 * x1 + 1.2 * x2 <= 8, name="joy_time_constraint")
    model.addConstr(0.3 * x1 + 0.6 * x2 <= 5, name="willa_time_constraint")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Number of pitchers of green tea: {x1.varValue}")
        print(f"Number of batches of pancakes: {x2.varValue}")
        print(f"Maximum profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```