## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Hank' and 'hours worked by Paul', which can be represented symbolically as $x_0$ and $x_1$ respectively.

## Step 2: Define the symbolic representation of the problem
The objective function to maximize is $2x_0 + 9x_1$.

## Step 3: List the constraints
The constraints given are:
- $27.19x_0 \leq 342$
- $17.72x_0 \leq 108$
- $22.33x_0 \leq 167$
- $23.57x_1 \leq 342$
- $23.11x_1 \leq 108$
- $15.33x_1 \leq 167$
- $27.19x_0 + 23.57x_1 \geq 167$
- $17.72x_0 + 23.11x_1 \geq 34$
- $22.33x_0 + 15.33x_1 \geq 67$
- $2x_0 - 10x_1 \geq 0$
- $27.19x_0 + 23.57x_1 \leq 229$
- $17.72x_0 + 23.11x_1 \leq 99$
- $22.33x_0 + 15.33x_1 \leq 92$

## 4: Convert the problem into a Gurobi code
We will use Gurobi to solve this linear programming problem.

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

# Create a new model
model = gurobi.Model()

# Define the variables
x0 = model.addVar(name="hours_worked_by_Hank", lb=0)
x1 = model.addVar(name="hours_worked_by_Paul", lb=0)

# Define the objective function
model.setObjective(2*x0 + 9*x1, gurobi.GRB.MAXIMIZE)

# Add constraints
model.addConstr(27.19*x0 <= 342, name="organization_score_Hank")
model.addConstr(17.72*x0 <= 108, name="likelihood_to_quit_Hank")
model.addConstr(22.33*x0 <= 167, name="work_quality_Hank")
model.addConstr(23.57*x1 <= 342, name="organization_score_Paul")
model.addConstr(23.11*x1 <= 108, name="likelihood_to_quit_Paul")
model.addConstr(15.33*x1 <= 167, name="work_quality_Paul")
model.addConstr(27.19*x0 + 23.57*x1 >= 167, name="combined_organization_score_min")
model.addConstr(17.72*x0 + 23.11*x1 >= 34, name="combined_likelihood_to_quit_min")
model.addConstr(22.33*x0 + 15.33*x1 >= 67, name="combined_work_quality_min")
model.addConstr(2*x0 - 10*x1 >= 0, name="Hank_Paul_hours_constraint")
model.addConstr(27.19*x0 + 23.57*x1 <= 229, name="combined_organization_score_max")
model.addConstr(17.72*x0 + 23.11*x1 <= 99, name="combined_likelihood_to_quit_max")
model.addConstr(22.33*x0 + 15.33*x1 <= 92, name="combined_work_quality_max")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by Hank: {x0.x}")
    print(f"Hours worked by Paul: {x1.x}")
    print(f"Objective function value: {model.objVal}")
else:
    print("No optimal solution found.")
```

## 6: Symbolic representation of the problem
```json
{
    'sym_variables': [('x0', 'hours worked by Hank'), ('x1', 'hours worked by Paul')],
    'objective_function': '2*x0 + 9*x1',
    'constraints': [
        '27.19*x0 <= 342',
        '17.72*x0 <= 108',
        '22.33*x0 <= 167',
        '23.57*x1 <= 342',
        '23.11*x1 <= 108',
        '15.33*x1 <= 167',
        '27.19*x0 + 23.57*x1 >= 167',
        '17.72*x0 + 23.11*x1 >= 34',
        '22.33*x0 + 15.33*x1 >= 67',
        '2*x0 - 10*x1 >= 0',
        '27.19*x0 + 23.57*x1 <= 229',
        '17.72*x0 + 23.11*x1 <= 99',
        '22.33*x0 + 15.33*x1 <= 92'
    ]
}
```