## Step 1: Define the optimization problem and identify the objective function.
The objective function to minimize is $5.11 \times \text{hours worked by Jean} + 6.35 \times \text{hours worked by Mary}$.

## 2: List all the constraints.
1. $\text{organization score of Jean} = 5$
2. $\text{dollar cost per hour of Jean} = 12$
3. $\text{computer competence rating of Jean} = 10$
4. $\text{paperwork competence rating of Jean} = 12$
5. $\text{organization score of Mary} = 1$
6. $\text{dollar cost per hour of Mary} = 4$
7. $\text{computer competence rating of Mary} = 7$
8. $\text{paperwork competence rating of Mary} = 14$
9. $5 \times \text{hours worked by Jean} + 1 \times \text{hours worked by Mary} \geq 19$
10. $12 \times \text{hours worked by Jean} + 4 \times \text{hours worked by Mary} \geq 18$
11. $10 \times \text{hours worked by Jean} + 7 \times \text{hours worked by Mary} \geq 21$
12. $12 \times \text{hours worked by Jean} + 14 \times \text{hours worked by Mary} \geq 10$
13. $8 \times \text{hours worked by Jean} - 1 \times \text{hours worked by Mary} \geq 0$
14. $5 \times \text{hours worked by Jean} + 1 \times \text{hours worked by Mary} \leq 34$
15. $12 \times \text{hours worked by Jean} + 4 \times \text{hours worked by Mary} \leq 31$
16. $10 \times \text{hours worked by Jean} + 7 \times \text{hours worked by Mary} \leq 52$
17. $12 \times \text{hours worked by Jean} + 14 \times \text{hours worked by Mary} \leq 42$

## 3: Convert the problem into Gurobi code.
We will use Gurobi's Python API to model and solve this problem.

```python
import gurobi

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

    # Define the variables
    jean_hours = model.addVar(name="jean_hours", lb=0)  # Assuming hours cannot be negative
    mary_hours = model.addVar(name="mary_hours", lb=0)  # Assuming hours cannot be negative

    # Define the objective function
    model.setObjective(5.11 * jean_hours + 6.35 * mary_hours, gurobi.GRB.MINIMIZE)

    # Define the constraints
    model.addConstr(5 * jean_hours + 1 * mary_hours >= 19, name="org_score_min")
    model.addConstr(12 * jean_hours + 4 * mary_hours >= 18, name="dollar_cost_min")
    model.addConstr(10 * jean_hours + 7 * mary_hours >= 21, name="comp_comp_min")
    model.addConstr(12 * jean_hours + 14 * mary_hours >= 10, name="paperwork_comp_min")
    model.addConstr(8 * jean_hours - 1 * mary_hours >= 0, name="jean_mary_hours_ratio")
    model.addConstr(5 * jean_hours + 1 * mary_hours <= 34, name="org_score_max")
    model.addConstr(12 * jean_hours + 4 * mary_hours <= 31, name="dollar_cost_max")
    model.addConstr(10 * jean_hours + 7 * mary_hours <= 52, name="comp_comp_max")
    model.addConstr(12 * jean_hours + 14 * mary_hours <= 42, name="paperwork_comp_max")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Hours worked by Jean: {jean_hours.varValue}")
        print(f"Hours worked by Mary: {mary_hours.varValue}")
        print(f"Objective Function Value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```