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

Let's define:
- $x_1$ as the hours worked by Bill,
- $x_2$ as the hours worked by John.

The objective function is to maximize: $4.03x_1 + 7.68x_2$

Given the constraints, we have:
1. Organization score constraint: $6.44x_1 + 5.84x_2 \geq 5$
2. Productivity rating constraint: $2.16x_1 + 2.06x_2 \geq 39$
3. Computer competence rating constraint: $4.71x_1 + 2.29x_2 \geq 7$
4. Additional linear constraint: $4x_1 - 7x_2 \geq 0$
5. Upper bound on organization score: $6.44x_1 + 5.84x_2 \leq 13$
6. Upper bound on productivity rating: $2.16x_1 + 2.06x_2 \leq 78$
7. Upper bound on computer competence rating: $4.71x_1 + 2.29x_2 \leq 15$

Symbolic representation:
```json
{
    'sym_variables': [('x1', 'hours worked by Bill'), ('x2', 'hours worked by John')],
    'objective_function': '4.03*x1 + 7.68*x2',
    'constraints': [
        '6.44*x1 + 5.84*x2 >= 5',
        '2.16*x1 + 2.06*x2 >= 39',
        '4.71*x1 + 2.29*x2 >= 7',
        '4*x1 - 7*x2 >= 0',
        '6.44*x1 + 5.84*x2 <= 13',
        '2.16*x1 + 2.06*x2 <= 78',
        '4.71*x1 + 2.29*x2 <= 15'
    ]
}
```

Now, let's implement this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define the variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="hours_worked_by_Bill")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="hours_worked_by_John")

# Set the objective function
m.setObjective(4.03*x1 + 7.68*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(6.44*x1 + 5.84*x2 >= 5, "organization_score_lower")
m.addConstr(2.16*x1 + 2.06*x2 >= 39, "productivity_rating_lower")
m.addConstr(4.71*x1 + 2.29*x2 >= 7, "computer_competence_rating_lower")
m.addConstr(4*x1 - 7*x2 >= 0, "additional_linear_constraint")
m.addConstr(6.44*x1 + 5.84*x2 <= 13, "organization_score_upper")
m.addConstr(2.16*x1 + 2.06*x2 <= 78, "productivity_rating_upper")
m.addConstr(4.71*x1 + 2.29*x2 <= 15, "computer_competence_rating_upper")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Bill: {x1.x}")
    print(f"Hours worked by John: {x2.x}")
else:
    print("No optimal solution found.")
```