## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'hours worked by Bobby' and 'hours worked by Mary'. Let's denote 'hours worked by Bobby' as $x_1$ and 'hours worked by Mary' as $x_2$. The objective function to minimize is $9.26x_1^2 + 9.08x_1x_2$.

## 2: List the constraints in symbolic notation
The constraints given are:
- $0.12x_1 + 0.75x_2 \geq 28$
- $0.34x_1 + 0.74x_2 \geq 22$
- $-10x_1 + 6x_2 \geq 0$
- $0.12x_1 + 0.75x_2 \leq 73$
- $0.34x_1 + 0.74x_2 \leq 109$

## 3: Define the symbolic representation
The symbolic variables are:
- $x_1$ for 'hours worked by Bobby'
- $x_2$ for 'hours worked by Mary'

The objective function is: $9.26x_1^2 + 9.08x_1x_2$

The constraints are:
- $0.12x_1 + 0.75x_2 \geq 28$
- $0.34x_1 + 0.74x_2 \geq 22$
- $-10x_1 + 6x_2 \geq 0$
- $0.12x_1 + 0.75x_2 \leq 73$
- $0.34x_1 + 0.74x_2 \leq 109$

## 4: Convert to JSON format for symbolic representation
```json
{
'sym_variables': [('x1', 'hours worked by Bobby'), ('x2', 'hours worked by Mary')],
'objective_function': '9.26*x1^2 + 9.08*x1*x2',
'constraints': [
'0.12*x1 + 0.75*x2 >= 28',
'0.34*x1 + 0.74*x2 >= 22',
'-10*x1 + 6*x2 >= 0',
'0.12*x1 + 0.75*x2 <= 73',
'0.34*x1 + 0.74*x2 <= 109'
]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi

def optimize_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="hours_worked_by_Bobby")
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="hours_worked_by_Mary")

    # Define the objective function
    model.setObjective(9.26 * x1**2 + 9.08 * x1 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(0.12 * x1 + 0.75 * x2 >= 28, name="organization_score_constraint")
    model.addConstr(0.34 * x1 + 0.74 * x2 >= 22, name="work_quality_rating_constraint")
    model.addConstr(-10 * x1 + 6 * x2 >= 0, name="hourly_work_constraint")
    model.addConstr(0.12 * x1 + 0.75 * x2 <= 73, name="organization_score_upper_bound")
    model.addConstr(0.34 * x1 + 0.74 * x2 <= 109, name="work_quality_rating_upper_bound")

    # Optimize the model
    model.optimize()

    # Print the status of the optimization
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Optimal solution found.")
        print("Hours worked by Bobby: ", x1.varValue)
        print("Hours worked by Mary: ", x2.varValue)
        print("Objective function value: ", model.objVal)
    elif model.status == gurobi.GRB.Status.INFEASIBLE:
        print("No feasible solution exists.")
    else:
        print("Optimization failed.")

optimize_problem()
```