To solve this optimization problem using Gurobi, we first need to understand and possibly simplify or clarify the constraints provided. The objective function aims to minimize the total cost, which is calculated as 6.49 times the hours worked by Laura plus 9.41 times the hours worked by Ringo.

Given:
- Objective Function: Minimize \(6.49 \times \text{hours worked by Laura} + 9.41 \times \text{hours worked by Ringo}\)
- Decision Variables: 
  - \(x_0\): Hours worked by Laura
  - \(x_1\): Hours worked by Ringo

Constraints:
1. Paperwork competence rating constraints:
   - Minimum combined rating: \(8x_0 + 4x_1 \geq 36\)
   - Maximum combined rating: \(8x_0 + 4x_1 \leq 60\)

2. Organization score constraints:
   - Minimum combined score: \(11x_0 + 7x_1 \geq 44\)
   - Maximum combined score: \(11x_0 + 7x_1 \leq 100\)

3. Productivity rating constraints:
   - Minimum combined rating: \(7x_0 + 2x_1 \geq 28\)
   - Maximum combined rating: \(7x_0 + 2x_1 \leq 54\)

4. Additional constraint: \(10x_0 - 5x_1 \geq 0\)

Since both decision variables are allowed to be fractional (not restricted to integers), we can model this problem as a linear programming problem.

Here is the Gurobi code that captures this optimization problem:

```python
from gurobipy import *

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

# Decision Variables
x0 = m.addVar(name='hours_worked_by_Laura', lb=0)  # Hours worked by Laura
x1 = m.addVar(name='hours_worked_by_Ringo', lb=0)  # Hours worked by Ringo

# Objective Function: Minimize the total cost
m.setObjective(6.49 * x0 + 9.41 * x1, GRB.MINIMIZE)

# Constraints
# Paperwork competence rating constraints
m.addConstr(8*x0 + 4*x1 >= 36, name='paperwork_min')
m.addConstr(8*x0 + 4*x1 <= 60, name='paperwork_max')

# Organization score constraints
m.addConstr(11*x0 + 7*x1 >= 44, name='organization_min')
m.addConstr(11*x0 + 7*x1 <= 100, name='organization_max')

# Productivity rating constraints
m.addConstr(7*x0 + 2*x1 >= 28, name='productivity_min')
m.addConstr(7*x0 + 2*x1 <= 54, name='productivity_max')

# Additional constraint
m.addConstr(10*x0 - 5*x1 >= 0, name='additional_constraint')

# Optimize the model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Laura: {x0.x}")
    print(f"Hours worked by Ringo: {x1.x}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found.")
```