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

## Step 2: Define the attributes or resources for each variable
The attributes are given as:
- $r_0$: organization score
- $r_1$: productivity rating
- $r_2$: computer competence rating
With specific values for Bill and John:
- Bill: $r_0 = 6.44$, $r_1 = 2.16$, $r_2 = 4.71$
- John: $r_0 = 5.84$, $r_1 = 2.06$, $r_2 = 2.29$

## 3: Formulate the objective function
The objective function to maximize is $4.03x_1 + 7.68x_2$.

## 4: Formulate the constraints
1. $6.44x_1 + 5.84x_2 \geq 5$
2. $2.16x_1 + 2.06x_2 \geq 39$
3. $4.71x_1 + 2.29x_2 \geq 7$
4. $4x_1 - 7x_2 \geq 0$
5. $6.44x_1 + 5.84x_2 \leq 13$
6. $2.16x_1 + 2.06x_2 \leq 78$
7. $4.71x_1 + 2.29x_2 \leq 15$

## 5: 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'
]
}
```

## 6: 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_Bill", lb=0)
    x2 = model.addVar(name="hours_worked_by_John", lb=0)

    # Objective function
    model.setObjective(4.03*x1 + 7.68*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(6.44*x1 + 5.84*x2 >= 5, name="organization_score_constraint")
    model.addConstr(2.16*x1 + 2.06*x2 >= 39, name="productivity_rating_constraint")
    model.addConstr(4.71*x1 + 2.29*x2 >= 7, name="computer_competence_rating_constraint")
    model.addConstr(4*x1 - 7*x2 >= 0, name="hours_worked_constraint")
    model.addConstr(6.44*x1 + 5.84*x2 <= 13, name="organization_score_upper_bound")
    model.addConstr(2.16*x1 + 2.06*x2 <= 78, name="productivity_rating_upper_bound")
    model.addConstr(4.71*x1 + 2.29*x2 <= 15, name="computer_competence_rating_upper_bound")

    # Optimize
    model.optimize()

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

solve_optimization_problem()
```