To solve the optimization problem described, we will use Gurobi, a powerful solver for linear and mixed-integer programming problems. The problem involves minimizing an objective function subject to several constraints, including bounds on the total usefulness ratings of various items and limitations on their quantities.

The objective function to minimize is: $9x_0 + 8x_1 + 6x_2$, where $x_0$ represents the quantity of cans of coffee, $x_1$ represents the quantity of rubber bands, and $x_2$ represents the quantity of headsets.

Given constraints:
- Usefulness ratings: 17 for cans of coffee, 16 for rubber bands, and 13 for headsets.
- Minimum total usefulness rating from cans of coffee plus rubber bands: 52.
- Minimum total usefulness rating from rubber bands plus headsets: 30.
- Minimum total combined usefulness rating from all items: 40 (specified twice but considered as one constraint).
- Constraint on the combination of cans of coffee and headsets: $6x_0 - 2x_2 \geq 0$.
- Maximum total usefulness rating from rubber bands plus headsets: 157.
- All quantities must be integers.

Here is how we translate these constraints into a Gurobi model:

```python
from gurobipy import *

# Create a model
m = Model("Optimization_Problem")

# Define variables
x0 = m.addVar(vtype=GRB.INTEGER, name="cans_of_coffee")
x1 = m.addVar(vtype=GRB.INTEGER, name="rubber_bands")
x2 = m.addVar(vtype=GRB.INTEGER, name="headsets")

# Objective function: Minimize 9*x0 + 8*x1 + 6*x2
m.setObjective(9*x0 + 8*x1 + 6*x2, GRB.MINIMIZE)

# Constraints
# Minimum total usefulness rating from cans of coffee plus rubber bands
m.addConstr(17*x0 + 16*x1 >= 52, name="usefulness_coffee_rubber")

# Minimum total usefulness rating from rubber bands plus headsets
m.addConstr(16*x1 + 13*x2 >= 30, name="usefulness_rubber_headsets")

# Minimum total combined usefulness rating from all items
m.addConstr(17*x0 + 16*x1 + 13*x2 >= 40, name="total_usefulness_min")

# Constraint on the combination of cans of coffee and headsets
m.addConstr(6*x0 - 2*x2 >= 0, name="coffee_headsets_constraint")

# Maximum total usefulness rating from rubber bands plus headsets
m.addConstr(16*x1 + 13*x2 <= 157, name="usefulness_rubber_headsets_max")

# Solve the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"cans_of_coffee: {x0.x}")
    print(f"rubber_bands: {x1.x}")
    print(f"headsets: {x2.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```

This code defines the optimization problem using Gurobi's Python interface, sets up all the specified constraints, and solves for the minimum of the objective function. The results are then printed out, including the quantities of each item in the optimal solution and the value of the objective function at this solution.