## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Paul', 'hours worked by Ringo', and 'hours worked by Bobby'. Let's denote them as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the natural language objects into symbolic notation
The symbolic representation of the variables is:
- $x_1$ for 'hours worked by Paul'
- $x_2$ for 'hours worked by Ringo'
- $x_3$ for 'hours worked by Bobby'

## 3: Define the objective function in symbolic notation
The objective function to minimize is $1.09x_1 + 1.75x_2 + 1.36x_3$.

## 4: List the constraints in symbolic notation
The constraints are:
- $8x_1 \leq 69$ (Implicit upper bound from $r0$ for Paul, but we directly use $x_0=8$ as a constant)
- $18x_2 \leq 69$ (Implicit upper bound from $r0$ for Ringo, but we directly use $x_1=18$ as a constant)
- $13x_3 \leq 69$ (Implicit upper bound from $r0$ for Bobby, but we directly use $x_2=13$ as a constant)
- $8x_1 + 13x_3 \geq 16$
- $8x_1 + 18x_2 \geq 9$
- $8x_1 + 18x_2 + 13x_3 \geq 9$
- $-8x_1 + 7x_3 \geq 0$
- $-8x_1 + 4x_2 \geq 0$
- $18x_2 + 13x_3 \leq 32$
- $8x_1 + 13x_3 \leq 52$

## 5: Consider variable bounds and types
- $x_1$ can be fractional
- $x_2$ is an integer
- $x_3$ can be fractional

## 6: Create the symbolic representation dictionary
```json
{
    'sym_variables': [('x1', 'hours worked by Paul'), ('x2', 'hours worked by Ringo'), ('x3', 'hours worked by Bobby')],
    'objective_function': '1.09*x1 + 1.75*x2 + 1.36*x3',
    'constraints': [
        '8*x1 + 13*x3 >= 16',
        '8*x1 + 18*x2 >= 9',
        '8*x1 + 18*x2 + 13*x3 >= 9',
        '-8*x1 + 7*x3 >= 0',
        '-8*x1 + 4*x2 >= 0',
        '18*x2 + 13*x3 <= 32',
        '8*x1 + 13*x3 <= 52'
    ]
}
```

## 7: Write the Gurobi code
```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="hours_worked_by_Paul", lb=0)  # No upper bound given, assuming continuous
    x2 = model.addVar(name="hours_worked_by_Ringo", lb=0, vtype=gurobi.GRB.INTEGER)  # Integer variable
    x3 = model.addVar(name="hours_worked_by_Bobby", lb=0)  # No upper bound given, assuming continuous

    # Objective function
    model.setObjective(1.09 * x1 + 1.75 * x2 + 1.36 * x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(8 * x1 + 13 * x3 >= 16)
    model.addConstr(8 * x1 + 18 * x2 >= 9)
    model.addConstr(8 * x1 + 18 * x2 + 13 * x3 >= 9)
    model.addConstr(-8 * x1 + 7 * x3 >= 0)
    model.addConstr(-8 * x1 + 4 * x2 >= 0)
    model.addConstr(18 * x2 + 13 * x3 <= 32)
    model.addConstr(8 * x1 + 13 * x3 <= 52)

    # Organization score constraints (Implicit in variable definition)
    # model.addConstr(x1 <= 69 / 8)  
    # model.addConstr(x2 <= 69 / 18)
    # model.addConstr(x3 <= 69 / 13)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by Paul: {x1.varValue}")
        print(f"Hours worked by Ringo: {x2.varValue}")
        print(f"Hours worked by Bobby: {x3.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```