To solve the given optimization problem using Gurobi, we first need to understand and possibly simplify the constraints provided. The objective function to minimize is \(9 \times \text{hours worked by John} + 6 \times \text{hours worked by Bobby}\).

Given variables:
- \(x_0\): hours worked by John
- \(x_1\): hours worked by Bobby

The constraints are as follows:
1. Productivity rating for John: 1
2. Computer competence rating for John: 6
3. Productivity rating for Bobby: 1
4. Computer competence rating for Bobby: 9
5. Combined productivity rating \(\geq 21\): \(x_0 + x_1 \geq 21\)
6. Combined computer competence rating \(\geq 24\): \(6x_0 + 9x_1 \geq 24\)
7. Constraint: \(-7x_0 + 4x_1 \geq 0\)
8. Combined productivity rating \(\leq 56\): \(x_0 + x_1 \leq 56\)
9. Combined computer competence rating \(\leq 42\): \(6x_0 + 9x_1 \leq 42\)

Note that constraints related to individual ratings (1, 2, 3, 4) are more about defining the coefficients for combined ratings rather than separate constraints.

Now, let's write the Gurobi code in Python to solve this optimization problem:

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_John")
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Bobby")

# Set the objective function
m.setObjective(9*x0 + 6*x1, GRB.MINIMIZE)

# Add constraints
m.addConstr(x0 + x1 >= 21, "Combined_Productivity_Rating_Min")
m.addConstr(6*x0 + 9*x1 >= 24, "Combined_Computer_Competence_Rating_Min")
m.addConstr(-7*x0 + 4*x1 >= 0, "Constraint_1")
m.addConstr(x0 + x1 <= 56, "Combined_Productivity_Rating_Max")
m.addConstr(6*x0 + 9*x1 <= 42, "Combined_Computer_Competence_Rating_Max")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print("Hours worked by John:", x0.x)
    print("Hours worked by Bobby:", x1.x)
    print("Objective function value:", m.objVal)
else:
    print("No optimal solution found")
```