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

Let's define:
- $x_0$ as the hours worked by Jean,
- $x_1$ as the hours worked by Mary.

The objective function is to minimize: $5.11x_0 + 6.35x_1$.

Given constraints can be summarized and translated into symbolic form as follows:

1. Organization score constraint: $5x_0 + x_1 \geq 19$
2. Dollar cost per hour constraint: $12x_0 + 4x_1 \geq 18$
3. Computer competence rating constraint: $10x_0 + 7x_1 \geq 21$
4. Paperwork competence rating constraint: $12x_0 + 14x_1 \geq 10$
5. Additional linear constraint: $8x_0 - x_1 \geq 0$
6. Upper bound on organization score: $5x_0 + x_1 \leq 34$
7. Upper bound on dollar cost per hour: $12x_0 + 4x_1 \leq 31$
8. Upper bound on computer competence rating: $10x_0 + 7x_1 \leq 52$
9. Upper bound on paperwork competence rating: $12x_0 + 14x_1 \leq 42$

Symbolic representation:
```json
{
    'sym_variables': [('x0', 'hours worked by Jean'), ('x1', 'hours worked by Mary')],
    'objective_function': '5.11*x0 + 6.35*x1',
    'constraints': [
        '5*x0 + x1 >= 19',
        '12*x0 + 4*x1 >= 18',
        '10*x0 + 7*x1 >= 21',
        '12*x0 + 14*x1 >= 10',
        '8*x0 - x1 >= 0',
        '5*x0 + x1 <= 34',
        '12*x0 + 4*x1 <= 31',
        '10*x0 + 7*x1 <= 52',
        '12*x0 + 14*x1 <= 42'
    ]
}
```

To solve this optimization problem using Gurobi, we can use the following Python code:

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(name='hours_worked_by_Jean', lb=0)
x1 = m.addVar(name='hours_worked_by_Mary', lb=0)

# Objective function: Minimize 5.11*x0 + 6.35*x1
m.setObjective(5.11*x0 + 6.35*x1, GRB.MINIMIZE)

# Constraints
m.addConstr(5*x0 + x1 >= 19, name='organization_score_constraint')
m.addConstr(12*x0 + 4*x1 >= 18, name='dollar_cost_per_hour_constraint')
m.addConstr(10*x0 + 7*x1 >= 21, name='computer_competence_rating_constraint')
m.addConstr(12*x0 + 14*x1 >= 10, name='paperwork_competence_rating_constraint')
m.addConstr(8*x0 - x1 >= 0, name='additional_linear_constraint')
m.addConstr(5*x0 + x1 <= 34, name='upper_bound_organization_score')
m.addConstr(12*x0 + 4*x1 <= 31, name='upper_bound_dollar_cost_per_hour')
m.addConstr(10*x0 + 7*x1 <= 52, name='upper_bound_computer_competence_rating')
m.addConstr(12*x0 + 14*x1 <= 42, name='upper_bound_paperwork_competence_rating')

# Optimize
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Jean: {x0.x}")
    print(f"Hours worked by Mary: {x1.x}")
else:
    print("No optimal solution found")
```