To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's denote:

- $x_1$ as the number of standing tables produced,
- $x_2$ as the number of dining tables produced.

The objective function is to maximize the total monthly profit, which can be represented as:
\[ 45x_1 + 95x_2 \]

Given the constraints:
1. Time for producing parts: $2x_1 + 4x_2 \leq 6000$
2. Time for assembling: $2.5x_1 + 1x_2 \leq 3000$
3. Time for polishing: $2x_1 + 1.5x_2 \leq 4500$

Non-negativity constraints:
- $x_1 \geq 0$
- $x_2 \geq 0$

The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'number of standing tables'), ('x2', 'number of dining tables')],
    'objective_function': '45*x1 + 95*x2',
    'constraints': [
        '2*x1 + 4*x2 <= 6000',
        '2.5*x1 + 1*x2 <= 3000',
        '2*x1 + 1.5*x2 <= 4500',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

Now, let's write the Gurobi code to solve this optimization problem:
```python
from gurobipy import *

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

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

# Set the objective function
m.setObjective(45*x1 + 95*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(2*x1 + 4*x2 <= 6000, "parts_production")
m.addConstr(2.5*x1 + x2 <= 3000, "assembling")
m.addConstr(2*x1 + 1.5*x2 <= 4500, "polishing")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of standing tables: {x1.x}")
    print(f"Number of dining tables: {x2.x}")
    print(f"Total profit: ${45*x1.x + 95*x2.x:.2f}")
else:
    print("No optimal solution found")
```