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

## Step 2: Define the symbolic representation of the problem
The objective function to maximize is $8x_1 + 5x_2$.

## Step 3: List all the constraints in symbolic notation
The constraints given are:
- $1x_1 + 22x_2 \geq 57$ (paperwork competence rating minimum)
- $5x_1 + 28x_2 \geq 31$ (organization score minimum)
- $11x_1 + 21x_2 \geq 43$ (dollar cost per hour minimum)
- $-3x_1 + 10x_2 \geq 0$ (linear combination of hours worked)
- $1x_1 + 22x_2 \leq 86$ (paperwork competence rating maximum)
- $5x_1 + 28x_2 \leq 124$ (organization score maximum)
- $11x_1 + 21x_2 \leq 60$ (dollar cost per hour maximum)
- $x_1, x_2 \geq 0$ (non-negativity, implicitly assumed as hours cannot be negative)

## 4: Correct and simplify the constraints based on the problem statement
Upon review, it seems there was an attempt to list constraints but let's ensure they align with the problem:
- The minimum paperwork competence rating: $1x_1 + 22x_2 \geq 57$
- The minimum organization score: $5x_1 + 28x_2 \geq 31$
- The minimum dollar cost per hour: $11x_1 + 21x_2 \geq 43$
- The linear combination: $-3x_1 + 10x_2 \geq 0$
- The maximum paperwork competence rating: $1x_1 + 22x_2 \leq 86$
- The maximum organization score: $5x_1 + 28x_2 \leq 124$
- The maximum dollar cost per hour: $11x_1 + 21x_2 \leq 60$

## 5: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [('x1', 'hours worked by John'), ('x2', 'hours worked by Paul')],
    'objective_function': '8*x1 + 5*x2',
    'constraints': [
        '1*x1 + 22*x2 >= 57',
        '5*x1 + 28*x2 >= 31',
        '11*x1 + 21*x2 >= 43',
        '-3*x1 + 10*x2 >= 0',
        '1*x1 + 22*x2 <= 86',
        '5*x1 + 28*x2 <= 124',
        '11*x1 + 21*x2 <= 60'
    ]
}
```

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

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

    # Define the variables
    x1 = model.addVar(name="hours_worked_by_John", lb=0)  # Assuming non-negativity
    x2 = model.addVar(name="hours_worked_by_Paul", lb=0)

    # Define the objective function
    model.setObjective(8 * x1 + 5 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(1 * x1 + 22 * x2 >= 57)  # paperwork competence rating minimum
    model.addConstr(5 * x1 + 28 * x2 >= 31)  # organization score minimum
    model.addConstr(11 * x1 + 21 * x2 >= 43)  # dollar cost per hour minimum
    model.addConstr(-3 * x1 + 10 * x2 >= 0)  # linear combination of hours worked
    model.addConstr(1 * x1 + 22 * x2 <= 86)  # paperwork competence rating maximum
    model.addConstr(5 * x1 + 28 * x2 <= 124)  # organization score maximum
    model.addConstr(11 * x1 + 21 * x2 <= 60)  # dollar cost per hour maximum

    # Optimize the model
    model.optimize()

    # Print the status of the model
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by John: {x1.x}")
        print(f"Hours worked by Paul: {x2.x}")
        print(f"Objective function value: {model.objVal}")
    elif model.status == gurobi.GRB.Status.INFEASIBLE:
        print("The model is infeasible.")
    else:
        print("The model has a non-optimal status.")

solve_optimization_problem()
```