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

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

## Step 3: Define the constraints in symbolic notation
The constraints given are:
1. $15x_1$ is not a constraint but a given attribute, similarly $4x_2$.
2. The total combined likelihood to quit index: $15x_1 + 4x_2 \geq 23$.
3. $-8x_1 + 3x_2 \geq 0$.
4. The total combined likelihood to quit index should be at maximum 84: $15x_1 + 4x_2 \leq 84$.

## 4: Consider the bounds of the likelihood to quit index
Given that $r0$ has an upper bound of 133, but specific bounds for $x_1$ and $x_2$ are not directly provided, we focus on the constraints directly mentioned.

## 5: Formulate the symbolic representation of the problem
The symbolic representation is:
- Variables: $x_1$ for 'hours worked by Ringo', $x_2$ for 'hours worked by Mary'.
- Objective function: Maximize $2x_1 + 8x_2$.
- Constraints:
  1. $15x_1 + 4x_2 \geq 23$.
  2. $-8x_1 + 3x_2 \geq 0$.
  3. $15x_1 + 4x_2 \leq 84$.

## 6: Convert the problem into a Gurobi model
We will use Gurobi to solve this linear programming problem.

```python
import gurobi as gp

# Create a new model
m = gp.Model("Optimization Problem")

# Define the variables
x1 = m.addVar(name="hours_worked_by_Ringo", lb=0)  # Assuming non-negative hours
x2 = m.addVar(name="hours_worked_by_Mary", lb=0)   # Assuming non-negative hours

# Define the objective function
m.setObjective(2*x1 + 8*x2, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(15*x1 + 4*x2 >= 23, name="likelihood_to_quit_index_min")
m.addConstr(-8*x1 + 3*x2 >= 0, name="hours_worked_constraint")
m.addConstr(15*x1 + 4*x2 <= 84, name="likelihood_to_quit_index_max")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by Ringo: {x1.varValue}")
    print(f"Hours worked by Mary: {x2.varValue}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```

## 7: Provide the symbolic representation in the required format
```json
{
    'sym_variables': [('x1', 'hours worked by Ringo'), ('x2', 'hours worked by Mary')],
    'objective_function': '2*x1 + 8*x2',
    'constraints': [
        '15*x1 + 4*x2 >= 23',
        '-8*x1 + 3*x2 >= 0',
        '15*x1 + 4*x2 <= 84'
    ]
}
```

```python
import gurobi as gp

# Create a new model
m = gp.Model("Optimization Problem")

# Define the variables
x1 = m.addVar(name="hours_worked_by_Ringo", lb=0)  
x2 = m.addVar(name="hours_worked_by_Mary", lb=0)   

# Define the objective function
m.setObjective(2*x1 + 8*x2, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(15*x1 + 4*x2 >= 23, name="likelihood_to_quit_index_min")
m.addConstr(-8*x1 + 3*x2 >= 0, name="hours_worked_constraint")
m.addConstr(15*x1 + 4*x2 <= 84, name="likelihood_to_quit_index_max")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by Ringo: {x1.varValue}")
    print(f"Hours worked by Mary: {x2.varValue}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```