To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables for the quantities of sheds and treehouses, formulating the objective function that represents the total profit, and listing all constraints related to building and painting time limitations.

Let's denote:
- \(x_1\) as the number of sheds,
- \(x_2\) as the number of treehouses.

The symbolic representation of the problem is thus:

```json
{
  'sym_variables': [('x1', 'number of sheds'), ('x2', 'number of treehouses')],
  'objective_function': '700*x1 + 500*x2',
  'constraints': [
    '4*x1 + 2*x2 <= 40',  # Building time constraint
    '2*x1 + 1.5*x2 <= 30'  # Painting time constraint
  ]
}
```

This representation captures the essence of the problem: maximizing profit (represented by the objective function `700*x1 + 500*x2`) under the constraints of limited building and painting time.

Now, to solve this optimization problem using Gurobi in Python, we will use the following code:

```python
from gurobipy import *

# Create a new model
m = Model("Sheds_and_Treehouses")

# Add variables
x1 = m.addVar(vtype=GRB.INTEGER, name="sheds")
x2 = m.addVar(vtype=GRB.INTEGER, name="treehouses")

# Set the objective function: Maximize profit
m.setObjective(700*x1 + 500*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(4*x1 + 2*x2 <= 40, "building_time")
m.addConstr(2*x1 + 1.5*x2 <= 30, "painting_time")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of sheds: {x1.x}")
    print(f"Number of treehouses: {x2.x}")
    print(f"Maximum profit: ${700*x1.x + 500*x2.x}")
else:
    print("No optimal solution found.")
```

This code defines the optimization problem using Gurobi's Python interface, solves it, and then prints out the optimal number of sheds and treehouses to build, along with the maximum achievable profit.