## Step 1: Define the symbolic representation of the problem
The problem involves minimizing an objective function subject to various constraints. The variables are:
- $x_0$: hours worked by Laura
- $x_1$: hours worked by Paul
- $x_2$: hours worked by Bill
- $x_3$: hours worked by John
- $x_4$: hours worked by George
- $x_5$: hours worked by Jean

## Step 2: Express the objective function in symbolic notation
The objective function to minimize is:
\[ 3.06x_0 + 7.24x_1 + 5.89x_2 + 6.62x_3 + 9.56x_4 + 6.55x_5 \]

## Step 3: List the constraints in symbolic notation
Constraints include:
- $2x_0 + 5x_1 + x_2 + 3x_3 + 9x_4 + 11x_5 \leq 183$ (paperwork competence rating)
- $4x_0 + x_1 + 6x_2 + 6x_3 + 9x_4 + 10x_5 \leq 267$ (organization score)
- $8x_0 + 11x_1 + 3x_2 + 3x_3 + 5x_4 + 7x_5 \leq 240$ (likelihood to quit index)
- $10x_0 + 6x_1 + 10x_2 + 2x_3 + 3x_4 + 9x_5 \leq 125$ (computer competence rating)
- $10x_0 + 11x_1 + 9x_2 + 11x_3 + 2x_4 + 5x_5 \leq 173$ (dollar cost per hour)
- And many more constraints as described

## 4: Provide a sample Gurobi code implementation
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="x0", lb=0, ub=None)  # hours worked by Laura
    x1 = model.addVar(name="x1", lb=0, ub=None)  # hours worked by Paul
    x2 = model.addVar(name="x2", lb=0, ub=None)  # hours worked by Bill
    x3 = model.addVar(name="x3", lb=0, ub=None)  # hours worked by John
    x4 = model.addVar(name="x4", lb=0, ub=None)  # hours worked by George
    x5 = model.addVar(name="x5", lb=0, ub=None)  # hours worked by Jean

    # Objective function
    model.setObjective(3.06*x0 + 7.24*x1 + 5.89*x2 + 6.62*x3 + 9.56*x4 + 6.55*x5, gurobi.GRB.MINIMIZE)

    # Constraints
    # Paperwork competence rating constraints
    model.addConstr(2*x0 + 5*x1 + x2 + 3*x3 + 9*x4 + 11*x5 <= 183)
    model.addConstr(2*x0 + 5*x1 <= 183 - x2 - 3*x3 - 9*x4 - 11*x5)
    # Organization score constraints
    model.addConstr(4*x0 + x1 + 6*x2 + 6*x3 + 9*x4 + 10*x5 <= 267)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Hours worked by Laura: ", x0.varValue)
        print("Hours worked by Paul: ", x1.varValue)
        print("Hours worked by Bill: ", x2.varValue)
        print("Hours worked by John: ", x3.varValue)
        print("Hours worked by George: ", x4.varValue)
        print("Hours worked by Jean: ", x5.varValue)
    else:
        print("No optimal solution found")

solve_optimization_problem()
```

## Step 5: Symbolic Representation
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Laura'),
        ('x1', 'hours worked by Paul'),
        ('x2', 'hours worked by Bill'),
        ('x3', 'hours worked by John'),
        ('x4', 'hours worked by George'),
        ('x5', 'hours worked by Jean')
    ],
    'objective_function': '3.06*x0 + 7.24*x1 + 5.89*x2 + 6.62*x3 + 9.56*x4 + 6.55*x5',
    'constraints': [
        '2*x0 + 5*x1 + x2 + 3*x3 + 9*x4 + 11*x5 <= 183',
        '4*x0 + x1 + 6*x2 + 6*x3 + 9*x4 + 10*x5 <= 267',
        '8*x0 + 11*x1 + 3*x2 + 3*x3 + 5*x4 + 7*x5 <= 240',
        '10*x0 + 6*x1 + 10*x2 + 2*x3 + 3*x4 + 9*x5 <= 125',
        '10*x0 + 11*x1 + 9*x2 + 11*x3 + 2*x4 + 5*x5 <= 173'
    ]
}
```