To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining the variables, the objective function, and the constraints using algebraic terms.

Let's denote:
- $x_1$ as the hours worked by Hank,
- $x_2$ as the hours worked by Mary,
- $x_3$ as the hours worked by Bobby.

The objective function to maximize is: $6x_1 + 7x_2 + 2x_3$.

The constraints are:
1. Total combined dollar cost per hour from all workers is at least 51: $23.13x_1 + 19.71x_2 + 7.57x_3 \geq 51$.
2. Constraint involving Hank and Bobby: $2x_1 - 3x_3 \geq 0$.
3. Total combined dollar cost per hour from Hank and Bobby is at most 114: $23.13x_1 + 7.57x_3 \leq 114$.
4. Total combined dollar cost per hour from Mary and Bobby is at most 109: $19.71x_2 + 7.57x_3 \leq 109$.
5. Total combined dollar cost per hour from all workers is at most 109: $23.13x_1 + 19.71x_2 + 7.57x_3 \leq 109$.

All variables are continuous, meaning they can take any real value (including fractions).

Given this symbolic representation, the problem in JSON format is:
```json
{
    'sym_variables': [('x1', 'hours worked by Hank'), ('x2', 'hours worked by Mary'), ('x3', 'hours worked by Bobby')],
    'objective_function': '6*x1 + 7*x2 + 2*x3',
    'constraints': [
        '23.13*x1 + 19.71*x2 + 7.57*x3 >= 51',
        '2*x1 - 3*x3 >= 0',
        '23.13*x1 + 7.57*x3 <= 114',
        '19.71*x2 + 7.57*x3 <= 109',
        '23.13*x1 + 19.71*x2 + 7.57*x3 <= 109'
    ]
}
```

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

```python
from gurobipy import *

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

# Define the variables
x1 = m.addVar(name="hours_worked_by_Hank", lb=0)
x2 = m.addVar(name="hours_worked_by_Mary", lb=0)
x3 = m.addVar(name="hours_worked_by_Bobby", lb=0)

# Set the objective function
m.setObjective(6*x1 + 7*x2 + 2*x3, GRB.MAXIMIZE)

# Add constraints
m.addConstr(23.13*x1 + 19.71*x2 + 7.57*x3 >= 51, name="total_cost_at_least_51")
m.addConstr(2*x1 - 3*x3 >= 0, name="hank_bobby_constraint")
m.addConstr(23.13*x1 + 7.57*x3 <= 114, name="hank_bobby_total_at_most_114")
m.addConstr(19.71*x2 + 7.57*x3 <= 109, name="mary_bobby_total_at_most_109")
m.addConstr(23.13*x1 + 19.71*x2 + 7.57*x3 <= 109, name="total_cost_at_most_109")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Hank: {x1.x}")
    print(f"Hours worked by Mary: {x2.x}")
    print(f"Hours worked by Bobby: {x3.x}")
else:
    print("No optimal solution found")
```