## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Paul' and 'hours worked by Bobby', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $6x_1 + 6x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
1. $6x_1 + 14x_2 \geq 21$
2. $6x_1 + 14x_2 \leq 74$
3. $9x_1 - 5x_2 \geq 0$
4. $x_1$ is an integer
5. $x_2$ is an integer

## 4: Convert the problem into a Gurobi-compatible format
We will use Gurobi's Python API to model and solve this problem.

## 5: Write the Gurobi code
```python
import gurobi as gp

# Create a new model
m = gp.Model()

# Define the variables
x1 = m.addVar(name="hours_worked_by_Paul", vtype=gp.GRB.INTEGER)  # Integer hours worked by Paul
x2 = m.addVar(name="hours_worked_by_Bobby", vtype=gp.GRB.INTEGER)  # Integer hours worked by Bobby

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

# Constraints
m.addConstr(6 * x1 + 14 * x2 >= 21, name="combined_work_quality_rating_min")
m.addConstr(6 * x1 + 14 * x2 <= 74, name="combined_work_quality_rating_max")
m.addConstr(9 * x1 - 5 * x2 >= 0, name="work_hours_constraint")

# Solve the model
m.optimize()

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

## 6: Provide the symbolic representation of the problem
```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',
        '6*x1 + 14*x2 <= 74',
        '9*x1 - 5*x2 >= 0',
        'x1 is an integer',
        'x2 is an integer'
    ]
}
```