To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints using mathematical notation.

Given:
- Variables: `x0` represents 'hours worked by John', `x1` represents 'hours worked by Bobby'.
- Objective Function: Minimize `3*x0 + 2*x1`.
- Constraints:
  1. Organization score constraint: `5*x0 + 8*x1 >= 7` and `5*x0 + 8*x1 <= 37`.
  2. Computer competence rating constraint: `13*x0 + x1 >= 8` and `13*x0 + x1 <= 16`.
  3. Additional linear constraint: `4*x0 - 8*x1 >= 0`.

The symbolic representation of the problem is:
```json
{
  'sym_variables': [('x0', 'hours worked by John'), ('x1', 'hours worked by Bobby')],
  'objective_function': 'Minimize 3*x0 + 2*x1',
  'constraints': [
    '5*x0 + 8*x1 >= 7',
    '5*x0 + 8*x1 <= 37',
    '13*x0 + x1 >= 8',
    '13*x0 + x1 <= 16',
    '4*x0 - 8*x1 >= 0'
  ]
}
```

Now, let's implement this optimization problem using Gurobi Python. Since `x0` and `x1` can be non-integer (as indicated by the possibility of a non-whole number of hours worked), we'll define them as continuous variables.

```python
from gurobipy import *

# Create a model
m = Model("Optimization_Problem")

# Define variables
x0 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="hours_worked_by_John")
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="hours_worked_by_Bobby")

# Set the objective function
m.setObjective(3*x0 + 2*x1, GRB.MINIMIZE)

# Add constraints
m.addConstr(5*x0 + 8*x1 >= 7, "organization_score_min")
m.addConstr(5*x0 + 8*x1 <= 37, "organization_score_max")
m.addConstr(13*x0 + x1 >= 8, "computer_competence_min")
m.addConstr(13*x0 + x1 <= 16, "computer_competence_max")
m.addConstr(4*x0 - 8*x1 >= 0, "additional_linear_constraint")

# Optimize the model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by John: {x0.x}")
    print(f"Hours worked by Bobby: {x1.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```