## Step 1: Define the symbolic representation of the problem

Let's denote:
- $x_1$ as the number of sheds
- $x_2$ as the number of treehouses

The objective is to maximize profit $P = 700x_1 + 500x_2$.

## Step 2: Identify the constraints

The constraints based on the given information are:
- Building time constraint: $4x_1 + 2x_2 \leq 40$
- Painting time constraint: $2x_1 + 1.5x_2 \leq 30$
- Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## 3: Symbolic representation in JSON format

```json
{
    'sym_variables': [('x1', 'sheds'), ('x2', 'treehouses')],
    'objective_function': '700*x1 + 500*x2',
    'constraints': [
        '4*x1 + 2*x2 <= 40',
        '2*x1 + 1.5*x2 <= 30',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Step 4: Convert the problem into Gurobi code

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(lb=0, name="sheds")
    x2 = model.addVar(lb=0, name="treehouses")

    # Objective function
    model.setObjective(700*x1 + 500*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(4*x1 + 2*x2 <= 40, name="building_time")
    model.addConstr(2*x1 + 1.5*x2 <= 30, name="painting_time")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: sheds = {x1.varValue}, treehouses = {x2.varValue}")
        print(f"Maximum profit: ${700*x1.varValue + 500*x2.varValue:.2f}")
    else:
        print("No optimal solution found")

solve_optimization_problem()
```