To solve the given optimization problem using Gurobi, we first need to translate the natural language description into a mathematical formulation that can be implemented in code. The objective function and constraints are defined as follows:

- Objective Function: Minimize \(8 \times (\text{hours worked by Laura})^2 + 6 \times (\text{hours worked by Jean})^2 + 1 \times (\text{hours worked by Laura})\)
- Variables:
  - \(L\) = hours worked by Laura
  - \(B\) = hours worked by Bobby
  - \(J\) = hours worked by Jean

Given constraints and their translations:

1. **Paperwork Competence Ratings**:
   - Laura: 12
   - Bobby: 6
   - Jean: 7

2. **Computer Competence Ratings**:
   - Laura: 6
   - Bobby: 16
   - Jean: 8

3. Constraints:
   - \(6B^2 + 7J^2 \geq 25\)
   - \(12L + 6B \geq 21\)
   - \(12L^2 + 6B^2 + 7J^2 \geq 54\)
   - \(12L + 6B + 7J \geq 54\)
   - \(6L + 16B \geq 40\)
   - \(16B + 8J \geq 98\)
   - \(6L + 16B + 8J \geq 98\)
   - \(4L^2 - 4J^2 \geq 0\)

All variables (\(L\), \(B\), \(J\)) can be non-integer.

Now, let's implement this problem in Gurobi using Python:

```python
from gurobipy import *

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

# Define the decision variables
L = m.addVar(name="hours_worked_by_Laura", lb=0)
B = m.addVar(name="hours_worked_by_Bobby", lb=0)
J = m.addVar(name="hours_worked_by_Jean", lb=0)

# Set the objective function
m.setObjective(8*L**2 + 6*J**2 + L, GRB.MINIMIZE)

# Add constraints
m.addConstr(6*B**2 + 7*J**2 >= 25, name="paperwork_combined_1")
m.addConstr(12*L + 6*B >= 21, name="paperwork_laura_bobby")
m.addConstr(12*L**2 + 6*B**2 + 7*J**2 >= 54, name="paperwork_squared_sum")
m.addConstr(12*L + 6*B + 7*J >= 54, name="paperwork_linear_sum")
m.addConstr(6*L + 16*B >= 40, name="computer_laura_bobby")
m.addConstr(16*B + 8*J >= 98, name="computer_bobby_jean")
m.addConstr(6*L + 16*B + 8*J >= 98, name="computer_total")
m.addConstr(4*L**2 - 4*J**2 >= 0, name="laura_jean_ratio")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by Laura: {L.x}")
    print(f"Hours worked by Bobby: {B.x}")
    print(f"Hours worked by Jean: {J.x}")
else:
    print("No optimal solution found.")
```