To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints using algebraic notation.

Let's denote:
- $x_1$ as 'hours worked by Mary'
- $x_2$ as 'hours worked by Ringo'

The objective function to minimize is: $6x_1 + 2x_2$

Given the constraints:
1. Organization score for Mary: $12x_1$
2. Productivity rating for Mary: $13x_1$
3. Organization score for Ringo: $19x_2$
4. Productivity rating for Ringo: $12x_2$
5. Combined organization score must be $\geq 24$: $12x_1 + 19x_2 \geq 24$
6. Since the minimum requirement is exactly 24, we can also consider it as an equality for optimization purposes: $12x_1 + 19x_2 = 24$
7. Combined productivity rating must be $\geq 25$: $13x_1 + 12x_2 \geq 25$
8. Again, considering the minimum requirement exactly: $13x_1 + 12x_2 = 25$
9. Constraint on hours worked: $9x_1 - 2x_2 \geq 0$
10. Maximum combined organization score: $12x_1 + 19x_2 \leq 62$
11. Maximum combined productivity rating: $13x_1 + 12x_2 \leq 121$

Since Mary's hours must be a whole number and Ringo's can be fractional, we have:
- $x_1$ is an integer
- $x_2$ is continuous

The symbolic representation of the problem in JSON format is:
```json
{
    'sym_variables': [('x1', 'hours worked by Mary'), ('x2', 'hours worked by Ringo')],
    'objective_function': '6*x1 + 2*x2',
    'constraints': [
        '12*x1 + 19*x2 >= 24',
        '13*x1 + 12*x2 >= 25',
        '9*x1 - 2*x2 >= 0',
        '12*x1 + 19*x2 <= 62',
        '13*x1 + 12*x2 <= 121'
    ]
}
```

Now, let's implement this in Gurobi Python code:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Mary")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Ringo")

# Set the objective function
m.setObjective(6*x1 + 2*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(12*x1 + 19*x2 >= 24, "Organization_Score_Min")
m.addConstr(13*x1 + 12*x2 >= 25, "Productivity_Rating_Min")
m.addConstr(9*x1 - 2*x2 >= 0, "Hours_Worked_Constraint")
m.addConstr(12*x1 + 19*x2 <= 62, "Organization_Score_Max")
m.addConstr(13*x1 + 12*x2 <= 121, "Productivity_Rating_Max")

# Optimize the model
m.optimize()

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