To tackle the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints in terms of these variables.

Let's denote:
- $x_1$ as the hours worked by Paul,
- $x_2$ as the hours worked by Bobby.

The objective function described is to minimize $6x_1 + 6x_2$.

Constraints are as follows:
1. The total combined work quality rating from hours worked by Paul and Bobby has to be at least 21: $6x_1 + 14x_2 \geq 21$.
2. The constraint that the total combined work quality rating must be at minimum 21 is already covered by the first constraint.
3. $9x_1 - 5x_2 \geq 0$.
4. The total combined work quality rating from hours worked by Paul and Bobby has to be at most 74: $6x_1 + 14x_2 \leq 74$.
5. $x_1$ must be an integer (hours worked by Paul).
6. $x_2$ must be a non-negative integer (hours worked by Bobby), which is implied by the context but not explicitly stated as a separate constraint beyond being non-fractional.

Given these definitions, our symbolic representation of the problem is:
```json
{
  'sym_variables': [('x1', 'hours worked by Paul'), ('x2', 'hours worked by Bobby')],
  'objective_function': '6*x1 + 6*x2',
  'constraints': [
    '6*x1 + 14*x2 >= 21',
    '9*x1 - 5*x2 >= 0',
    '6*x1 + 14*x2 <= 74'
  ]
}
```

Now, let's implement this optimization problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Paul")
x2 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Bobby")

# Set objective function
m.setObjective(6*x1 + 6*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(6*x1 + 14*x2 >= 21, name="work_quality_rating_min")
m.addConstr(9*x1 - 5*x2 >= 0, name="hours_worked_constraint")
m.addConstr(6*x1 + 14*x2 <= 74, name="work_quality_rating_max")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Paul: {x1.x}")
    print(f"Hours worked by Bobby: {x2.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```