## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the area in square feet for aster flowers.
- $x_2$ represents the area in square feet for stonecrops.

## Step 2: Formulate the objective function
The profit per square foot of aster flowers is $60, and the profit per square foot of stonecrops is $80. The objective function to maximize profit is:
\[ \text{Maximize:} \quad 60x_1 + 80x_2 \]

## 3: Define the constraints
1. The total area constraint: $x_1 + x_2 \leq 120$ (since James has 120 square feet available).
2. The budget constraint: $20x_1 + 45x_2 \leq 5000$ (since the seed for aster costs $20 per square foot and for stonecrops costs $45 per square foot, and James has a budget of $5000).
3. Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$ (since the area cannot be negative).

## 4: Symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'aster flowers area'), ('x2', 'stonecrops area')],
'objective_function': '60*x1 + 80*x2',
'constraints': ['x1 + x2 <= 120', '20*x1 + 45*x2 <= 5000', 'x1 >= 0', 'x2 >= 0']
}
```

## 5: Gurobi code to solve the optimization problem
```python
import gurobi

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

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

    # Define the objective function
    model.setObjective(60*x1 + 80*x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(x1 + x2 <= 120, name="total_area_constraint")
    model.addConstr(20*x1 + 45*x2 <= 5000, name="budget_constraint")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Aster flowers area: {x1.varValue}")
        print(f"Stonecrops area: {x2.varValue}")
        print(f"Max profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```