## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Hank', 'hours worked by Mary', 'hours worked by George', 'hours worked by Dale', which can be represented symbolically as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $7x_0 + 1x_1 + 6x_2 + 8x_3$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $10x_0 \leq 174$ (organization score for Hank, but this seems to be an attribute, not a constraint on $x_0$ directly)
- $7x_0 \leq 170$ (likelihood to quit index for Hank, similarly, an attribute)
- $7x_1 \leq 174$ and $13x_1 \leq 170$ (organization score and likelihood to quit for Mary)
- $12x_2 \leq 174$ and $13x_2 \leq 170$ (organization score and likelihood to quit for George)
- $8x_3 \leq 174$ and $6x_3 \leq 170$ (organization score and likelihood to quit for Dale)
- $7x_1 + 12x_2 \geq 29$ (combined organization score for Mary and George)
- $7x_0 + 6x_3 \geq 17$ (combined likelihood to quit index for Hank and Dale)
- $13x_1 + 6x_3 \geq 14$ (combined likelihood to quit index for Mary and Dale)
- $7x_0 + 13x_2 \geq 15$ (combined likelihood to quit index for Hank and George)
- $13x_1 + 13x_2 \geq 38$ (combined likelihood to quit index for Mary and George)
- $7x_0 + 13x_1 + 6x_3 \geq 40$ (combined likelihood to quit index for Hank, Mary, and Dale)
- $7x_0 + 13x_1 + 13x_2 \geq 40$ (combined likelihood to quit index for Hank, Mary, and George)
- $13x_1 + 13x_2 + 6x_3 \geq 40$ (combined likelihood to quit index for Mary, George, and Dale)
- $7x_0 + 13x_1 + 6x_3 \geq 35$ (another combined likelihood to quit index for Hank, Mary, and Dale)
- $7x_0 + 13x_1 + 13x_2 \geq 35$ (another combined likelihood to quit index for Hank, Mary, and George)
- $13x_1 + 13x_2 + 6x_3 \geq 35$ (another combined likelihood to quit index for Mary, George, and Dale)
- $13x_1 + 6x_3 \geq 21$ (combined likelihood to quit index for Mary and Dale)
- $7x_0 + 13x_1 + 13x_2 \geq 21$ (combined likelihood to quit index for Hank, Mary, and George)
- $13x_1 + 13x_2 + 6x_3 \geq 21$ (combined likelihood to quit index for Mary, George, and Dale)
- $10x_0 + 7x_1 \leq 155$ (combined organization score for Hank and Mary)
- $12x_2 + 8x_3 \leq 153$ (combined organization score for George and Dale)
- $10x_0 + 8x_3 \leq 157$ (combined organization score for Hank and Dale)
- $7x_1 + 12x_2 \leq 78$ (combined organization score for Mary and George)
- $7x_1 + 8x_3 \leq 69$ (combined organization score for Mary and Dale)
- $10x_0 + 7x_1 + 12x_2 + 8x_3 \leq 69$ (combined organization score for all)
- $13x_1 + 13x_2 \leq 93$ (combined likelihood to quit index for Mary and George)
- $7x_0 + 13x_2 \leq 99$ (combined likelihood to quit index for Hank and George)
- $7x_0 + 13x_1 + 6x_3 \leq 89$ (combined likelihood to quit index for Hank, Mary, and Dale)
- $7x_0 + 13x_1 + 13x_2 + 6x_3 \leq 89$ (combined likelihood to quit index for all)

## 4: Correct and Simplify Constraints
Correcting and simplifying, we note that individual scores are attributes, not constraints. Thus, we focus on the constraints provided:
- $7x_1 + 12x_2 \geq 29$
- $7x_0 + 6x_3 \geq 17$
- $13x_1 + 6x_3 \geq 14$
- $7x_0 + 13x_2 \geq 15$
- $13x_1 + 13x_2 \geq 38$
- $7x_0 + 13x_1 + 6x_3 \geq 40$
- $7x_0 + 13x_1 + 13x_2 \geq 40$
- $13x_1 + 13x_2 + 6x_3 \geq 40$
- $7x_0 + 13x_1 + 6x_3 \geq 35$
- $7x_0 + 13x_1 + 13x_2 \geq 35$
- $13x_1 + 13x_2 + 6x_3 \geq 35$
- $13x_1 + 6x_3 \geq 21$
- $7x_0 + 13x_1 + 13x_2 \geq 21$
- $13x_1 + 13x_2 + 6x_3 \geq 21$
- $10x_0 + 7x_1 \leq 155$
- $12x_2 + 8x_3 \leq 153$
- $10x_0 + 8x_3 \leq 157$
- $7x_1 + 12x_2 \leq 78$
- $7x_1 + 8x_3 \leq 69$
- $10x_0 + 7x_1 + 12x_2 + 8x_3 \leq 69$
- $13x_1 + 13x_2 \leq 93$
- $7x_0 + 13x_2 \leq 99$
- $7x_0 + 13x_1 + 6x_3 \leq 89$
- $7x_0 + 13x_1 + 13x_2 + 6x_3 \leq 89$

## 5: Symbolic Representation
The symbolic representation is:
```json
{
    'sym_variables': [('x0', 'hours worked by Hank'), ('x1', 'hours worked by Mary'), ('x2', 'hours worked by George'), ('x3', 'hours worked by Dale')],
    'objective_function': '7*x0 + 1*x1 + 6*x2 + 8*x3',
    'constraints': [
        '7*x1 + 12*x2 >= 29',
        '7*x0 + 6*x3 >= 17',
        '13*x1 + 6*x3 >= 14',
        '7*x0 + 13*x2 >= 15',
        '13*x1 + 13*x2 >= 38',
        '7*x0 + 13*x1 + 6*x3 >= 40',
        '7*x0 + 13*x1 + 13*x2 >= 40',
        '13*x1 + 13*x2 + 6*x3 >= 40',
        '7*x0 + 13*x1 + 6*x3 >= 35',
        '7*x0 + 13*x1 + 13*x2 >= 35',
        '13*x1 + 13*x2 + 6*x3 >= 35',
        '13*x1 + 6*x3 >= 21',
        '7*x0 + 13*x1 + 13*x2 >= 21',
        '13*x1 + 13*x2 + 6*x3 >= 21',
        '10*x0 + 7*x1 <= 155',
        '12*x2 + 8*x3 <= 153',
        '10*x0 + 8*x3 <= 157',
        '7*x1 + 12*x2 <= 78',
        '7*x1 + 8*x3 <= 69',
        '10*x0 + 7*x1 + 12*x2 + 8*x3 <= 69',
        '13*x1 + 13*x2 <= 93',
        '7*x0 + 13*x2 <= 99',
        '7*x0 + 13*x1 + 6*x3 <= 89',
        '7*x0 + 13*x1 + 13*x2 + 6*x3 <= 89'
    ]
}
```

## 6: Gurobi Code
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()
    
    # Define variables
    x0 = model.addVar(name="x0", lb=0)  # hours worked by Hank
    x1 = model.addVar(name="x1", lb=0)  # hours worked by Mary
    x2 = model.addVar(name="x2", lb=0)  # hours worked by George
    x3 = model.addVar(name="x3", lb=0)  # hours worked by Dale

    # Objective function
    model.setObjective(7*x0 + x1 + 6*x2 + 8*x3, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(7*x1 + 12*x2 >= 29)
    model.addConstr(7*x0 + 6*x3 >= 17)
    model.addConstr(13*x1 + 6*x3 >= 14)
    model.addConstr(7*x0 + 13*x2 >= 15)
    model.addConstr(13*x1 + 13*x2 >= 38)
    model.addConstr(7*x0 + 13*x1 + 6*x3 >= 40)
    model.addConstr(7*x0 + 13*x1 + 13*x2 >= 40)
    model.addConstr(13*x1 + 13*x2 + 6*x3 >= 40)
    model.addConstr(7*x0 + 13*x1 + 6*x3 >= 35)
    model.addConstr(7*x0 + 13*x1 + 13*x2 >= 35)
    model.addConstr(13*x1 + 13*x2 + 6*x3 >= 35)
    model.addConstr(13*x1 + 6*x3 >= 21)
    model.addConstr(7*x0 + 13*x1 + 13*x2 >= 21)
    model.addConstr(13*x1 + 13*x2 + 6*x3 >= 21)
    model.addConstr(10*x0 + 7*x1 <= 155)
    model.addConstr(12*x2 + 8*x3 <= 153)
    model.addConstr(10*x0 + 8*x3 <= 157)
    model.addConstr(7*x1 + 12*x2 <= 78)
    model.addConstr(7*x1 + 8*x3 <= 69)
    model.addConstr(10*x0 + 7*x1 + 12*x2 + 8*x3 <= 69)
    model.addConstr(13*x1 + 13*x2 <= 93)
    model.addConstr(7*x0 + 13*x2 <= 99)
    model.addConstr(7*x0 + 13*x1 + 6*x3 <= 89)
    model.addConstr(7*x0 + 13*x1 + 13*x2 + 6*x3 <= 89)

    # Solve the model
    model.optimize()

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

solve_optimization_problem()
```