To solve this optimization problem using Gurobi, we first need to translate the given natural language description into a mathematical formulation. The objective is to minimize the cost function $7x_0 + 4x_1$, where $x_0$ represents the hours worked by Dale and $x_1$ represents the hours worked by George.

Given constraints can be formulated as follows:
1. Paperwork competence rating: $7.09x_0 + 5.38x_1 \geq 49$
2. Dollar cost per hour: $4.11x_0 + 6.11x_1 \geq 45$
3. Work quality rating: $2.68x_0 + 4.9x_1 \geq 95$
4. Likelihood to quit index: $0.85x_0 + 3.05x_1 \geq 63$
5. Additional linear constraint: $-10x_0 + 3x_1 \geq 0$
6. Upper bound on paperwork competence rating: $7.09x_0 + 5.38x_1 \leq 119$
7. Upper bound on dollar cost per hour: $4.11x_0 + 6.11x_1 \leq 109$
8. Upper bound on work quality rating: $2.68x_0 + 4.9x_1 \leq 169$
9. Upper bound on likelihood to quit index: $0.85x_0 + 3.05x_1 \leq 109$

Since $x_0$ can be fractional but $x_1$ must be an integer, we'll define $x_0$ as a continuous variable and $x_1$ as an integer variable in Gurobi.

Here is the Python code using Gurobi to solve this optimization problem:

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Dale")
x1 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_George")

# Objective function: minimize 7*x0 + 4*x1
m.setObjective(7*x0 + 4*x1, GRB.MINIMIZE)

# Constraints
m.addConstr(7.09*x0 + 5.38*x1 >= 49, name="paperwork_competence_rating_min")
m.addConstr(4.11*x0 + 6.11*x1 >= 45, name="dollar_cost_per_hour_min")
m.addConstr(2.68*x0 + 4.9*x1 >= 95, name="work_quality_rating_min")
m.addConstr(0.85*x0 + 3.05*x1 >= 63, name="likelihood_to_quit_index_min")
m.addConstr(-10*x0 + 3*x1 >= 0, name="additional_linear_constraint")
m.addConstr(7.09*x0 + 5.38*x1 <= 119, name="paperwork_competence_rating_max")
m.addConstr(4.11*x0 + 6.11*x1 <= 109, name="dollar_cost_per_hour_max")
m.addConstr(2.68*x0 + 4.9*x1 <= 169, name="work_quality_rating_max")
m.addConstr(0.85*x0 + 3.05*x1 <= 109, name="likelihood_to_quit_index_max")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print("Hours worked by Dale:", x0.x)
    print("Hours worked by George:", x1.x)
    print("Objective function value:", m.objVal)
else:
    print("No optimal solution found")
```