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

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $3x_1 + 2x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
- $5x_1 \geq 5$ (John's organization score is 5, but this seems to be an attribute and not a constraint on $x_1$ directly. It seems we actually have $x_1$'s organization score contribution as 5 and $x_2$'s as 8. So, we consider the total organization score constraint: $5x_1 + 8x_2 \geq 7$ and $5x_1 + 8x_2 \leq 47$),
- $13x_1 \geq 13$ (similarly, this is an attribute, and we consider the total computer competence rating constraint: $13x_1 + 1x_2 \geq 8$ and $13x_1 + 1x_2 \leq 29$),
- $4x_1 - 8x_2 \geq 0$,
- $5x_1 + 8x_2 \leq 47$,
- $13x_1 + x_2 \leq 29$.

Correcting for accurate representation:
- The organization score constraints: $5x_1 + 8x_2 \geq 7$ and $5x_1 + 8x_2 \leq 47$,
- The computer competence rating constraints: $13x_1 + x_2 \geq 8$ and $13x_1 + x_2 \leq 29$,
- And $4x_1 - 8x_2 \geq 0$.

## 4: Formulate the symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'hours worked by John'), ('x2', 'hours worked by Bobby')],
'objective_function': '3*x1 + 2*x2',
'constraints': [
    '5*x1 + 8*x2 >= 7',
    '5*x1 + 8*x2 <= 47',
    '13*x1 + x2 >= 8',
    '13*x1 + x2 <= 29',
    '4*x1 - 8*x2 >= 0'
]
}
```

## 5: Implement the 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 hours cannot be negative
    x2 = model.addVar(name="hours_worked_by_Bobby", lb=0)  # Assuming hours cannot be negative

    # Define the objective function
    model.setObjective(3*x1 + 2*x2, gurobi.MINIMIZE)

    # Add constraints
    model.addConstr(5*x1 + 8*x2 >= 7, name="org_score_min")
    model.addConstr(5*x1 + 8*x2 <= 47, name="org_score_max")
    model.addConstr(13*x1 + x2 >= 8, name="comp_comp_min")
    model.addConstr(13*x1 + x2 <= 29, name="comp_comp_max")
    model.addConstr(4*x1 - 8*x2 >= 0, name="hourly_constraint")

    # Optimize the model
    model.optimize()

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

solve_optimization_problem()
```