To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables for each item of interest (hours worked by Ringo and Dale), formulating the objective function using these variables, and listing all constraints in terms of these variables.

Let's denote:
- \(x_1\) as the hours worked by Ringo,
- \(x_2\) as the hours worked by Dale.

The objective function to minimize is: \(7.11x_1^2 + 7.12x_2^2 + 7.13x_1\).

Constraints are:
1. Likelihood to quit index for Ringo: \(20x_1 \geq 53\) (However, this seems initially misstated; we'll correct it in the process as it likely should relate to a combination of both or individual constraints not directly given).
2. Organization score for Ringo: \(10x_1\).
3. Likelihood to quit index for Dale: \(18x_2\).
4. Organization score for Dale: \(16x_2\).
5. Combined likelihood to quit index: \(20x_1 + 18x_2 \geq 53\) (Correcting the interpretation to reflect a combined effect).
6. Combined organization score: \(10x_1 + 16x_2 \geq 40\).
7. Another constraint on scores and hours: \(9x_1 - 6x_2 \geq 0\).
8. Upper bound on combined likelihood to quit index: \(20x_1 + 18x_2 \leq 94\).
9. Upper bound on combined organization score: \(10x_1 + 16x_2 \leq 116\).

Given these, the symbolic representation of our problem 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', 
        '10*x1 + 16*x2 >= 40', 
        '9*x1 - 6*x2 >= 0', 
        '20*x1 + 18*x2 <= 94', 
        '10*x1 + 16*x2 <= 116'
    ]
}
```

Now, let's write the Gurobi code to solve this optimization problem:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Add variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Ringo")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Dale")

# Set the objective function
m.setObjective(7.11*x1**2 + 7.12*x2**2 + 7.13*x1, GRB.MINIMIZE)

# Add constraints
m.addConstr(20*x1 + 18*x2 >= 53, name="Combined_Likelihood_Lower_Bound")
m.addConstr(10*x1 + 16*x2 >= 40, name="Combined_Organization_Score_Lower_Bound")
m.addConstr(9*x1 - 6*x2 >= 0, name="Score_and_Hours_Constraint")
m.addConstr(20*x1 + 18*x2 <= 94, name="Combined_Likelihood_Upper_Bound")
m.addConstr(10*x1 + 16*x2 <= 116, name="Combined_Organization_Score_Upper_Bound")

# Optimize the model
m.optimize()

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