## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Peggy', 'hours worked by Bobby', 'hours worked by Bill', 'hours worked by George'] which can be represented symbolically as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Define the symbolic representation of the problem
The objective function to maximize is $7x_0 + 6x_1 + 4x_2 + 4x_3$.

## Step 3: List the constraints
The constraints given are:
- $0.56x_0 \leq 222$ (Peggy's computer competence rating constraint, but it's an attribute and not directly a constraint on $x_0$)
- $0.47x_0 \leq 124$ (Peggy's likelihood to quit index constraint)
- $0.61x_1 \leq 222$ (Bobby's computer competence rating constraint)
- $0.29x_1 \leq 124$ (Bobby's likelihood to quit index constraint)
- $0.41x_2 \leq 222$ (Bill's computer competence rating constraint)
- $1.32x_2 \leq 124$ (Bill's likelihood to quit index constraint)
- $1.81x_3 \leq 222$ (George's computer competence rating constraint)
- $0.09x_3 \leq 124$ (George's likelihood to quit index constraint)
- $0.56x_0 + 0.41x_2 \leq 137$ (Combined computer competence rating constraint for Peggy and Bill)
- $0.61x_1 + 1.81x_3 \leq 121$ (Combined computer competence rating constraint for Bobby and George)
- $0.56x_0 + 0.61x_1 \leq 163$ (Combined computer competence rating constraint for Peggy and Bobby)
- $0.41x_2 + 1.81x_3 \leq 181$ (Combined computer competence rating constraint for Bill and George)
- $0.56x_0 + 0.61x_1 + 0.41x_2 + 1.81x_3 \leq 181$ (Combined computer competence rating constraint for all)
- $0.29x_1 + 0.09x_3 \leq 111$ (Combined likelihood to quit index constraint for Bobby and George)
- $0.47x_0 + 1.32x_2 \leq 33$ (Combined likelihood to quit index constraint for Peggy and Bill)
- $0.47x_0 + 0.09x_3 \leq 82$ (Combined likelihood to quit index constraint for Peggy and George)
- $1.32x_2 + 0.09x_3 \leq 78$ (Combined likelihood to quit index constraint for Bill and George)
- $0.47x_0 + 0.29x_1 + 1.32x_2 + 0.09x_3 \leq 78$ (Combined likelihood to quit index constraint for all)

## Step 4: Create the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Peggy'),
        ('x1', 'hours worked by Bobby'),
        ('x2', 'hours worked by Bill'),
        ('x3', 'hours worked by George')
    ],
    'objective_function': '7*x0 + 6*x1 + 4*x2 + 4*x3',
    'constraints': [
        '0.56*x0 <= 222',
        '0.47*x0 <= 124',
        '0.61*x1 <= 222',
        '0.29*x1 <= 124',
        '0.41*x2 <= 222',
        '1.32*x2 <= 124',
        '1.81*x3 <= 222',
        '0.09*x3 <= 124',
        '0.56*x0 + 0.41*x2 <= 137',
        '0.61*x1 + 1.81*x3 <= 121',
        '0.56*x0 + 0.61*x1 <= 163',
        '0.41*x2 + 1.81*x3 <= 181',
        '0.56*x0 + 0.61*x1 + 0.41*x2 + 1.81*x3 <= 181',
        '0.29*x1 + 0.09*x3 <= 111',
        '0.47*x0 + 1.32*x2 <= 33',
        '0.47*x0 + 0.09*x3 <= 82',
        '1.32*x2 + 0.09*x3 <= 78',
        '0.47*x0 + 0.29*x1 + 1.32*x2 + 0.09*x3 <= 78'
    ]
}
```

## 5: Implement the problem in Gurobi
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x0 = model.addVar(name="x0", lb=0)  # hours worked by Peggy
    x1 = model.addVar(name="x1", lb=0)  # hours worked by Bobby
    x2 = model.addVar(name="x2", lb=0)  # hours worked by Bill
    x3 = model.addVar(name="x3", lb=0)  # hours worked by George

    # Define the objective function
    model.setObjective(7 * x0 + 6 * x1 + 4 * x2 + 4 * x3, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(0.56 * x0 <= 222)
    model.addConstr(0.47 * x0 <= 124)
    model.addConstr(0.61 * x1 <= 222)
    model.addConstr(0.29 * x1 <= 124)
    model.addConstr(0.41 * x2 <= 222)
    model.addConstr(1.32 * x2 <= 124)
    model.addConstr(1.81 * x3 <= 222)
    model.addConstr(0.09 * x3 <= 124)
    model.addConstr(0.56 * x0 + 0.41 * x2 <= 137)
    model.addConstr(0.61 * x1 + 1.81 * x3 <= 121)
    model.addConstr(0.56 * x0 + 0.61 * x1 <= 163)
    model.addConstr(0.41 * x2 + 1.81 * x3 <= 181)
    model.addConstr(0.56 * x0 + 0.61 * x1 + 0.41 * x2 + 1.81 * x3 <= 181)
    model.addConstr(0.29 * x1 + 0.09 * x3 <= 111)
    model.addConstr(0.47 * x0 + 1.32 * x2 <= 33)
    model.addConstr(0.47 * x0 + 0.09 * x3 <= 82)
    model.addConstr(1.32 * x2 + 0.09 * x3 <= 78)
    model.addConstr(0.47 * x0 + 0.29 * x1 + 1.32 * x2 + 0.09 * x3 <= 78)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Hours worked by Peggy: ", x0.varValue)
        print("Hours worked by Bobby: ", x1.varValue)
        print("Hours worked by Bill: ", x2.varValue)
        print("Hours worked by George: ", x3.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```