To solve the given optimization problem, we need to define the decision variables, objective function, and constraints in a way that Gurobi can understand. The decision variables are 'hours worked by Jean', 'hours worked by George', and 'hours worked by Dale'. We will denote these as `Jean`, `George`, and `Dale` respectively.

The objective function to minimize is: $6.28 \times (\text{hours worked by Jean})^2 + 4.64 \times (\text{hours worked by Dale})^2 + 2.73 \times (\text{hours worked by Jean})$.

Given constraints are:
1. Productivity ratings for each person.
2. Paperwork competence ratings for each person.
3. Minimum combined productivity rating from George and Dale.
4. Minimum combined productivity rating from all three.
5. Minimum combined paperwork competence rating from Jean and George.
6. Minimum combined paperwork competence rating from all three.
7. A linear constraint involving hours worked by Jean and George.
8. Maximum combined paperwork competence rating from Jean and Dale.
9. Maximum combined paperwork competence rating from George and Dale.

All variables can be fractional (continuous), so we don't need integer constraints for any of them.

Here's how the problem can be represented in Gurobi:

```python
from gurobipy import *

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

# Define decision variables
Jean = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name='hours_worked_by_Jean')
George = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name='hours_worked_by_George')
Dale = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name='hours_worked_by_Dale')

# Objective function
m.setObjective(6.28 * Jean**2 + 4.64 * Dale**2 + 2.73 * Jean, GRB.MINIMIZE)

# Constraints
m.addConstr(Jean * 7 + George * 1 + Dale * 17 >= 42, name='combined_productivity_all')
m.addConstr(George * 1 + Dale * 17 >= 42, name='combined_productivity_GD')
m.addConstr(Jean * 16 + George * 10 >= 49, name='paperwork_competence_JG_min')
m.addConstr(Jean * 16 + George * 10 + Dale * 5 >= 49, name='paperwork_competence_all_min')
m.addConstr(-4 * Jean + 10 * George >= 0, name='linear_constraint')
m.addConstr(Jean * 16 + Dale * 5 <= 125, name='paperwork_competence_JD_max')
m.addConstr(George * 10 + Dale * 5 <= 143, name='paperwork_competence_GD_max')

# Solve the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print('Optimal solution found:')
    print(f'Hours worked by Jean: {Jean.x}')
    print(f'Hours worked by George: {George.x}')
    print(f'Hours worked by Dale: {Dale.x}')
else:
    print('No optimal solution found')
```