To solve the optimization problem described, we first need to convert the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the given information.

Let's denote:
- $x_1$ as the number of houses cleaned,
- $x_2$ as the number of apartments cleaned.

The profit per house cleaned is $300, and the profit per apartment cleaned is $250. Therefore, the objective function to maximize profit can be written as:
\[ \text{Maximize:} \quad 300x_1 + 250x_2 \]

Given the constraints:
- Each house requires 2 hours of sweeping, and each apartment requires 1 hour of sweeping. The company has available 600 hours for sweeping. Thus, the sweeping constraint is:
\[ 2x_1 + x_2 \leq 600 \]
- Each house requires 2 hours of mopping, and each apartment requires 1.5 hours of mopping. The company has available 700 hours for mopping. Thus, the mopping constraint is:
\[ 2x_1 + 1.5x_2 \leq 700 \]
- Additionally, $x_1$ and $x_2$ must be non-negative since they represent quantities of houses and apartments.

The symbolic representation in JSON format is:
```json
{
    'sym_variables': [('x1', 'number of houses cleaned'), ('x2', 'number of apartments cleaned')],
    'objective_function': '300*x1 + 250*x2',
    'constraints': ['2*x1 + x2 <= 600', '2*x1 + 1.5*x2 <= 700', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this optimization problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.INTEGER, name="houses_cleaned")
x2 = m.addVar(lb=0, vtype=GRB.INTEGER, name="apartments_cleaned")

# Set the objective function
m.setObjective(300*x1 + 250*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(2*x1 + x2 <= 600, "sweeping_hours")
m.addConstr(2*x1 + 1.5*x2 <= 700, "mopping_hours")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Houses cleaned: {x1.x}")
    print(f"Apartments cleaned: {x2.x}")
    print(f"Maximum profit: ${300*x1.x + 250*x2.x:.2f}")
else:
    print("No optimal solution found")
```