## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Bobby' and 'hours worked by Hank', which can be represented symbolically as $x_1$ and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $2x_1 + 9x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
1. $6x_1 + 5x_2 \geq 14$
2. $10x_1 - 9x_2 \geq 0$
3. $6x_1 + 5x_2 \leq 39$
4. The organization scores for Bobby and Hank are constants, not constraints on $x_1$ and $x_2$ but rather $x_1 \geq 0$, $x_2 \geq 0$ since hours worked cannot be negative.

## 4: Consider the organization score constraint
The total combined organization score from hours worked by Bobby and Hank must be within certain limits, but the scores themselves (6 for Bobby, 5 for Hank) seem to be part of the coefficients in the constraints rather than limits on $x_1$ and $x_2$. Thus, we focus on the constraints provided.

## 5: Create the symbolic representation of the problem
The symbolic representation is:
- Variables: $(x_1, x_2)$ corresponding to ('hours worked by Bobby', 'hours worked by Hank')
- Objective function: $2x_1 + 9x_2$
- Constraints:
1. $6x_1 + 5x_2 \geq 14$
2. $10x_1 - 9x_2 \geq 0$
3. $6x_1 + 5x_2 \leq 39$
4. $x_1 \geq 0$, $x_2 \geq 0$ (implicit non-negativity)

## 6: Convert the problem into Gurobi code
```python
import gurobi

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

# Define the variables
x1 = model.addVar(lb=0, name="hours_worked_by_Bobby")  # hours worked by Bobby
x2 = model.addVar(lb=0, name="hours_worked_by_Hank")  # hours worked by Hank

# Define the objective function
model.setObjective(2*x1 + 9*x2, gurobi.GRB.MAXIMIZE)

# Add constraints
model.addConstr(6*x1 + 5*x2 >= 14, name="org_score_min")
model.addConstr(10*x1 - 9*x2 >= 0, name="hours_worked_constraint")
model.addConstr(6*x1 + 5*x2 <= 39, name="org_score_max")

# Optimize the model
model.optimize()

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

## 7: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [('x1', 'hours worked by Bobby'), ('x2', 'hours worked by Hank')],
    'objective_function': '2*x1 + 9*x2',
    'constraints': [
        '6*x1 + 5*x2 >= 14',
        '10*x1 - 9*x2 >= 0',
        '6*x1 + 5*x2 <= 39',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```