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.

Let's define:
- $x_1$ as 'hours worked by John'
- $x_2$ as 'hours worked by Mary'

The objective function is to minimize $9x_1 + 2x_2$.

Given the constraints:
1. The total combined paperwork competence rating from hours worked by John and Mary must be at least 20: $5x_1 + 8x_2 \geq 20$
2. The constraint is repeated, so we acknowledge it but do not duplicate it in our list.
3. The total combined organization score from hours worked by John and Mary has to be 14 or more: $2x_1 + 8x_2 \geq 14$
4. This constraint is also repeated, so it's acknowledged without duplication.
5. $5x_1 - 4x_2 \geq 0$
6. The total combined paperwork competence rating from hours worked by John and Mary must be at maximum 45: $5x_1 + 8x_2 \leq 45$
7. The total combined organization score from hours worked by John and Mary must be as much or less than 45: $2x_1 + 8x_2 \leq 45$

Symbolic representation:
```json
{
    'sym_variables': [('x1', 'hours worked by John'), ('x2', 'hours worked by Mary')],
    'objective_function': '9*x1 + 2*x2',
    'constraints': [
        '5*x1 + 8*x2 >= 20',
        '2*x1 + 8*x2 >= 14',
        '5*x1 - 4*x2 >= 0',
        '5*x1 + 8*x2 <= 45',
        '2*x1 + 8*x2 <= 45'
    ]
}
```

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

```python
from gurobipy import *

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

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

# Set the objective function
m.setObjective(9*x1 + 2*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(5*x1 + 8*x2 >= 20, "paperwork_competence_rating")
m.addConstr(2*x1 + 8*x2 >= 14, "organization_score_min")
m.addConstr(5*x1 - 4*x2 >= 0, "mixed_constraint")
m.addConstr(5*x1 + 8*x2 <= 45, "paperwork_competence_rating_max")
m.addConstr(2*x1 + 8*x2 <= 45, "organization_score_max")

# Optimize the model
m.optimize()

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