## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'hours worked by Ringo' and 'hours worked by Dale'. Let's denote 'hours worked by Ringo' as $x_1$ and 'hours worked by Dale' as $x_2$. The objective function to minimize is $7.11x_1^2 + 7.12x_2^2 + 7.13x_1$.

## Step 2: List the constraints in symbolic notation
The constraints given are:
- $r0: 20x_1 + 18x_2 \geq 53$ (likelihood to quit index from hours worked)
- $r0: 20x_1^2 + 18x_2^2 \geq 53$ (combined likelihood to quit index from hours worked squared)
- $r1: 10x_1 + 16x_2 \geq 40$ (organization score from hours worked)
- $r1: 10x_1^2 + 16x_2^2 \geq 40$ (combined organization score from hours worked squared)
- $9x_1 - 6x_2 \geq 0$
- $20x_1 + 18x_2 \leq 94$ (total combined likelihood to quit index)
- $10x_1 + 16x_2 \leq 116$ (total combined organization score)

## 3: Create a symbolic representation of the problem
The symbolic representation is:
```json
{
'sym_variables': [('x1', 'hours worked by Ringo'), ('x2', 'hours worked by Dale')],
'objective_function': '7.11*x1^2 + 7.12*x2^2 + 7.13*x1',
'constraints': [
    '20*x1 + 18*x2 >= 53',
    '20*x1^2 + 18*x2^2 >= 53',
    '10*x1 + 16*x2 >= 40',
    '10*x1^2 + 16*x2^2 >= 40',
    '9*x1 - 6*x2 >= 0',
    '20*x1 + 18*x2 <= 94',
    '10*x1 + 16*x2 <= 116'
]
}
```

## 4: Implement the problem in Gurobi
Now, let's implement this problem in Gurobi using Python.

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="hours_worked_by_Ringo", lb=0)  # Assuming hours cannot be negative
    x2 = model.addVar(name="hours_worked_by_Dale", lb=0)

    # Define the objective function
    model.setObjective(7.11 * x1**2 + 7.12 * x2**2 + 7.13 * x1, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(20 * x1 + 18 * x2 >= 53, name="likelihood_to_quit_index")
    model.addConstr(20 * x1**2 + 18 * x2**2 >= 53, name="combined_likelihood_to_quit_index_squared")
    model.addConstr(10 * x1 + 16 * x2 >= 40, name="organization_score")
    model.addConstr(10 * x1**2 + 16 * x2**2 >= 40, name="combined_organization_score_squared")
    model.addConstr(9 * x1 - 6 * x2 >= 0, name="ringo_dale_hours_constraint")
    model.addConstr(20 * x1 + 18 * x2 <= 94, name="max_likelihood_to_quit_index")
    model.addConstr(10 * x1 + 16 * x2 <= 116, name="max_organization_score")

    # Update the model
    model.update()

    # Solve the model
    model.optimize()

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

optimization_problem()
```