## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The goal is to maximize the total monthly profit by determining the optimal number of standing tables and dining tables to manufacture.

Let's define the decision variables:

* $x_1$: number of standing tables to produce
* $x_2$: number of dining tables to produce

The objective function is to maximize the total profit:

* Profit per standing table: $45
* Profit per dining table: $95

The constraints are:

* Producing parts: 2 hours for a standing table, 4 hours for a dining table, with a total of 6000 hours available
* Assembling: 2.5 hours for a standing table, 1 hour for a dining table, with a total of 3000 hours available
* Polishing: 2 hours for a standing table, 1.5 hours for a dining table, with a total of 4500 hours available

## Mathematical Formulation

The mathematical formulation of the problem is:

Maximize:

$$45x_1 + 95x_2$$

Subject to:

$$2x_1 + 4x_2 \leq 6000$$
$$2.5x_1 + x_2 \leq 3000$$
$$2x_1 + 1.5x_2 \leq 4500$$
$$x_1, x_2 \geq 0$$

## Gurobi Code

```python
import gurobi

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

    # Define the decision variables
    x1 = model.addVar(name="standing_tables", lb=0, ub=None, obj=45)
    x2 = model.addVar(name="dining_tables", lb=0, ub=None, obj=95)

    # Define the constraints
    model.addConstr(2 * x1 + 4 * x2 <= 6000, name="parts_production")
    model.addConstr(2.5 * x1 + x2 <= 3000, name="assembly")
    model.addConstr(2 * x1 + 1.5 * x2 <= 4500, name="polishing")

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

    # Optimize the model
    model.optimize()

    # Print the results
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Standing tables: {x1.x}")
        print(f"Dining tables: {x2.x}")
        print(f"Total profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_table_production_problem()
```