## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the number of coffee tables produced
- $x_2$ represents the number of bedside tables produced

## Step 2: Formulate the objective function
The profit made on a coffee table is $50, and the profit on a bedside table is $90. The objective function to maximize the total monthly profit is:
\[ \text{Maximize:} \quad 50x_1 + 90x_2 \]

## 3: Define the constraints
Based on the problem description, we have the following constraints:
- Producing the parts: $2.5x_1 + 4.5x_2 \leq 6500$
- Assembling the parts: $3x_1 + 2x_2 \leq 3500$
- Polishing the tables: $1.5x_1 + 3.5x_2 \leq 5000$
- Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## 4: Symbolic representation of the problem
The symbolic representation is:
```json
{
    'sym_variables': [('x1', 'coffee tables'), ('x2', 'bedside tables')],
    'objective_function': '50*x1 + 90*x2',
    'constraints': [
        '2.5*x1 + 4.5*x2 <= 6500',
        '3*x1 + 2*x2 <= 3500',
        '1.5*x1 + 3.5*x2 <= 5000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## 5: Convert to Gurobi code in Python
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(name="coffee_tables", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(name="bedside_tables", lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Set the objective function
    model.setObjective(50 * x1 + 90 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(2.5 * x1 + 4.5 * x2 <= 6500, name="parts_production")
    model.addConstr(3 * x1 + 2 * x2 <= 3500, name="parts_assembly")
    model.addConstr(1.5 * x1 + 3.5 * x2 <= 5000, name="tables_polishing")

    # Optimize the model
    model.optimize()

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

solve_optimization_problem()
```