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

## Step 2: Define the symbolic representation of the problem
The objective function to maximize is $9x_1 + 6x_2$.

## Step 3: List all the constraints in symbolic notation
- $10x_1 + 14x_2 \geq 26$ (total combined paperwork competence rating)
- $1x_1 + 9x_2 \geq 8$ (total combined computer competence rating)
- $14x_1 + 12x_2 \geq 12$ (total combined dollar cost per hour)
- $12x_1 + 14x_2 \geq 6$ (total combined work quality rating)
- $2x_1 - 2x_2 \geq 0$ (relationship between hours worked by Peggy and Laura)
- $10x_1 + 14x_2 \leq 73$ (upper bound on total combined paperwork competence rating)
- $1x_1 + 9x_2 \leq 25$ (upper bound on total combined computer competence rating)
- $14x_1 + 12x_2 \leq 30$ (upper bound on total combined dollar cost per hour)
- $12x_1 + 14x_2 \leq 40$ (upper bound on total combined work quality rating)

## 4: Create the symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'hours worked by Peggy'), ('x2', 'hours worked by Laura')],
'objective_function': '9*x1 + 6*x2',
'constraints': [
    '10*x1 + 14*x2 >= 26',
    '1*x1 + 9*x2 >= 8',
    '14*x1 + 12*x2 >= 12',
    '12*x1 + 14*x2 >= 6',
    '2*x1 - 2*x2 >= 0',
    '10*x1 + 14*x2 <= 73',
    '1*x1 + 9*x2 <= 25',
    '14*x1 + 12*x2 <= 30',
    '12*x1 + 14*x2 <= 40'
]
}
```

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

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

    # Define the variables
    x1 = model.addVar(name="hours_worked_by_Peggy", lb=0)  # hours worked by Peggy
    x2 = model.addVar(name="hours_worked_by_Laura", lb=0)  # hours worked by Laura

    # Define the objective function
    model.setObjective(9 * x1 + 6 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(10 * x1 + 14 * x2 >= 26)  # total combined paperwork competence rating
    model.addConstr(1 * x1 + 9 * x2 >= 8)  # total combined computer competence rating
    model.addConstr(14 * x1 + 12 * x2 >= 12)  # total combined dollar cost per hour
    model.addConstr(12 * x1 + 14 * x2 >= 6)  # total combined work quality rating
    model.addConstr(2 * x1 - 2 * x2 >= 0)  # relationship between hours worked by Peggy and Laura
    model.addConstr(10 * x1 + 14 * x2 <= 73)  # upper bound on total combined paperwork competence rating
    model.addConstr(1 * x1 + 9 * x2 <= 25)  # upper bound on total combined computer competence rating
    model.addConstr(14 * x1 + 12 * x2 <= 30)  # upper bound on total combined dollar cost per hour
    model.addConstr(12 * x1 + 14 * x2 <= 40)  # upper bound on total combined work quality rating

    # Optimize the model
    model.optimize()

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

solve_optimization_problem()
```