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

## Step 2: Define the symbolic representation of the problem
The objective function to maximize is $7x_0 + 7x_1 + 9x_2$.

## Step 3: List the constraints
The constraints given are:
- $13x_0 \geq 13$ (Mary's likelihood to quit index is 13, but this seems to be an attribute, not a constraint in the traditional sense. It should be $x_0 \geq 0$ and similar for others, but let's assume it's about using the attributes properly)
- $12x_0 \geq 12$ (Mary's computer competence rating is 12, similar issue)
- $8x_0 \geq 8$ (Mary's dollar cost per hour is 8, similar issue)
- $8x_1 \geq 8$ (George's likelihood to quit index is 8)
- $8x_1 \geq 8$ (George's computer competence rating is 8)
- $8x_1 \geq 8$ (George's dollar cost per hour is 8)
- $5x_2 \geq 5$ (Peggy's likelihood to quit index is 5)
- $9x_2 \geq 9$ (Peggy's computer competence rating is 9)
- $5x_2 \geq 5$ (Peggy's dollar cost per hour is 5)
- $13x_0 + 8x_1 \geq 38$ (total combined likelihood to quit index from hours worked by Mary and George)
- $8x_1 + 5x_2 \geq 49$ (total combined likelihood to quit index from hours worked by George and Peggy)
- $8x_0 + 8x_1 + 5x_2 \geq 18$ (total combined dollar cost per hour)
- $13x_0 + 5x_2 \leq 93$ (total combined likelihood to quit index from hours worked by Mary and Peggy)
- $13x_0 + 8x_1 + 5x_2 \leq 93$ (total combined likelihood to quit index from all)
- $12x_0 + 9x_2 \leq 205$ (total combined computer competence rating from hours worked by Mary and Peggy)
- $8x_1 + 9x_2 \leq 129$ (total combined computer competence rating from hours worked by George and Peggy)
- $12x_0 + 8x_1 + 9x_2 \leq 129$ (total combined computer competence rating from all)
- $8x_0 + 8x_1 \leq 57$ (total combined dollar cost per hour from Mary and George)
- $8x_1 + 5x_2 \leq 39$ (total combined dollar cost per hour from George and Peggy)
- $8x_0 + 8x_1 + 5x_2 \leq 39$ (total combined dollar cost per hour from all)

## 4: Correctly interpret the constraints and variables
Given that $x_0$, $x_1$, and $x_2$ represent hours worked by Mary, George, and Peggy respectively, and considering the attributes:
- $r0 = \{13, 8, 5\}$ for likelihood to quit index,
- $r1 = \{12, 8, 9\}$ for computer competence rating,
- $r2 = \{8, 8, 5\}$ for dollar cost per hour,

The correct constraints should directly utilize these attributes without misinterpretation.

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

# Create a new model
m = gurobi.Model()

# Define the variables
x0 = m.addVar(name="x0", lb=0, ub=None)  # hours worked by Mary
x1 = m.addVar(name="x1", lb=0, ub=None, integrality=gurobi.GRB.INTEGER)  # hours worked by George
x2 = m.addVar(name="x2", lb=0, ub=None)  # hours worked by Peggy

# Objective function
m.setObjective(7*x0 + 7*x1 + 9*x2, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(13*x0 + 8*x1 >= 38)  # likelihood to quit index from Mary and George
m.addConstr(8*x1 + 5*x2 >= 49)  # likelihood to quit index from George and Peggy
m.addConstr(8*x0 + 8*x1 + 5*x2 >= 18)  # dollar cost per hour from all
m.addConstr(13*x0 + 5*x2 <= 93)  # likelihood to quit index from Mary and Peggy
m.addConstr(13*x0 + 8*x1 + 5*x2 <= 93)  # likelihood to quit index from all
m.addConstr(12*x0 + 9*x2 <= 205)  # computer competence rating from Mary and Peggy
m.addConstr(8*x1 + 9*x2 <= 129)  # computer competence rating from George and Peggy
m.addConstr(12*x0 + 8*x1 + 9*x2 <= 129)  # computer competence rating from all
m.addConstr(8*x0 + 8*x1 <= 57)  # dollar cost per hour from Mary and George
m.addConstr(8*x1 + 5*x2 <= 39)  # dollar cost per hour from George and Peggy
m.addConstr(8*x0 + 8*x1 + 5*x2 <= 39)  # dollar cost per hour from all

# Optimize the model
m.optimize()

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

## 6: Symbolic Representation
```json
{
    'sym_variables': [('x0', 'hours worked by Mary'), ('x1', 'hours worked by George'), ('x2', 'hours worked by Peggy')],
    'objective_function': '7*x0 + 7*x1 + 9*x2',
    'constraints': [
        '13*x0 + 8*x1 >= 38',
        '8*x1 + 5*x2 >= 49',
        '8*x0 + 8*x1 + 5*x2 >= 18',
        '13*x0 + 5*x2 <= 93',
        '13*x0 + 8*x1 + 5*x2 <= 93',
        '12*x0 + 9*x2 <= 205',
        '8*x1 + 9*x2 <= 129',
        '12*x0 + 8*x1 + 9*x2 <= 129',
        '8*x0 + 8*x1 <= 57',
        '8*x1 + 5*x2 <= 39',
        '8*x0 + 8*x1 + 5*x2 <= 39'
    ]
}
```