## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by George', 'hours worked by John', 'hours worked by Jean', 'hours worked by Bobby'].
Let's denote them as $x_1, x_2, x_3, x_4$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $3x_1 + 6x_2 + 5x_3 + 1x_4$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $10x_1 \leq 273$ (George's computer competence rating)
- $4x_2 \leq 273$ (John's computer competence rating)
- $6x_3 \leq 273$ (Jean's computer competence rating)
- $9x_4 \leq 273$ (Bobby's computer competence rating)
- $4x_2 + 6x_3 + 9x_4 \geq 45$
- $10x_1 + 4x_2 + 6x_3 \geq 45$
- $4x_2 + 6x_3 + 9x_4 \geq 50$
- $10x_1 + 4x_2 + 6x_3 \geq 50$
- $10x_1 + 4x_2 \leq 240$
- $6x_3 + 9x_4 \leq 265$
- $10x_1 + 4x_2 + 9x_4 \leq 175$
- $10x_1 + 4x_2 + 6x_3 + 9x_4 \leq 175$
- $x_1$ is an integer
- $x_3$ is an integer

## Step 4: Create the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'hours worked by George'), 
        ('x2', 'hours worked by John'), 
        ('x3', 'hours worked by Jean'), 
        ('x4', 'hours worked by Bobby')
    ], 
    'objective_function': '3*x1 + 6*x2 + 5*x3 + 1*x4', 
    'constraints': [
        '10*x1 <= 273', 
        '4*x2 <= 273', 
        '6*x3 <= 273', 
        '9*x4 <= 273', 
        '4*x2 + 6*x3 + 9*x4 >= 45', 
        '10*x1 + 4*x2 + 6*x3 >= 45', 
        '4*x2 + 6*x3 + 9*x4 >= 50', 
        '10*x1 + 4*x2 + 6*x3 >= 50', 
        '10*x1 + 4*x2 <= 240', 
        '6*x3 + 9*x4 <= 265', 
        '10*x1 + 4*x2 + 9*x4 <= 175', 
        '10*x1 + 4*x2 + 6*x3 + 9*x4 <= 175', 
        'x1 % 1 == 0', 
        'x3 % 1 == 0'
    ]
}
```

## Step 5: Write the Gurobi code
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()

    # Define variables
    x1 = model.addVar(name='hours_worked_by_George', vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name='hours_worked_by_John')
    x3 = model.addVar(name='hours_worked_by_Jean', vtype=gurobi.GRB.INTEGER)
    x4 = model.addVar(name='hours_worked_by_Bobby')

    # Objective function
    model.setObjective(3*x1 + 6*x2 + 5*x3 + x4, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(10*x1 <= 273)
    model.addConstr(4*x2 <= 273)
    model.addConstr(6*x3 <= 273)
    model.addConstr(9*x4 <= 273)
    model.addConstr(4*x2 + 6*x3 + 9*x4 >= 45)
    model.addConstr(10*x1 + 4*x2 + 6*x3 >= 45)
    model.addConstr(4*x2 + 6*x3 + 9*x4 >= 50)
    model.addConstr(10*x1 + 4*x2 + 6*x3 >= 50)
    model.addConstr(10*x1 + 4*x2 <= 240)
    model.addConstr(6*x3 + 9*x4 <= 265)
    model.addConstr(10*x1 + 4*x2 + 9*x4 <= 175)
    model.addConstr(10*x1 + 4*x2 + 6*x3 + 9*x4 <= 175)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objval)
        print('Hours worked by George: ', x1.varValue)
        print('Hours worked by John: ', x2.varValue)
        print('Hours worked by Jean: ', x3.varValue)
        print('Hours worked by Bobby: ', x4.varValue)
    else:
        print('No solution found')

solve_optimization_problem()
```