## Step 1: Define the optimization problem and its components
The problem is a quadratic optimization problem with multiple constraints. We have three variables: $x_0$ (hours worked by George), $x_1$ (hours worked by Bill), and $x_2$ (hours worked by Laura). The objective function to minimize is $8x_0^2 + 8x_0x_1 + 8x_0x_2 + 9x_1^2 + 6x_1x_2 + x_2^2 + 3x_0 + 4x_1 + 5x_2$.

## Step 2: List all the constraints
1. $26x_0 \leq 200$
2. $5x_0 \leq 138$
3. $20x_0 \leq 233$
4. $1x_0 \leq 219$
5. $3x_0 \leq 198$
6. $3x_1 \leq 200$
7. $15x_1 \leq 138$
8. $24x_1 \leq 233$
9. $23x_1 \leq 219$
10. $12x_1 \leq 198$
11. $22x_2 \leq 200$
12. $12x_2 \leq 138$
13. $19x_2 \leq 233$
14. $29x_2 \leq 219$
15. $3x_2 \leq 198$
16. $3x_1^2 + 22x_2^2 \geq 64$
17. $26x_0 + 3x_1 + 22x_2 \geq 64$
18. $15x_1 + 12x_2 \geq 16$
19. $5x_0^2 + 12x_2^2 \geq 37$
20. $5x_0 + 15x_1 + 12x_2 \geq 37$
21. $20x_0^2 + 19x_2^2 \geq 77$
22. $20x_0 + 24x_1 \geq 74$
23. $20x_0 + 24x_1 + 19x_2 \geq 74$
24. $1x_0 + 23x_1 \geq 29$
25. $23x_1 + 29x_2 \geq 61$
26. $1x_0^2 + 23x_1^2 + 29x_2^2 \geq 72$
27. $1x_0 + 23x_1 + 29x_2 \geq 72$
28. $3x_0 + 3x_2 \geq 58$
29. $12x_1 + 3x_2 \geq 54$
30. $3x_0 + 12x_1 + 3x_2 \geq 54$
31. $10x_0^2 - 8x_2^2 \geq 0$
32. $9x_0 - 4x_1 \geq 0$
33. $26x_0 + 3x_1 \leq 111$
34. $5x_0 + 12x_2 \leq 115$
35. $12x_1 + 3x_2 \leq 111$
36. $x_0 \in \mathbb{Z}$ (integer)
37. $x_1 \in \mathbb{R}$ (float)
38. $x_2 \in \mathbb{R}$ (float)

## Step 3: Implement the optimization problem using Gurobi
We will use the Gurobi Python API to model and solve this problem.

```python
import gurobi as gp
from gurobi import GRB

# Create a new model
m = gp.Model("optimization_problem")

# Define the variables
x0 = m.addVar(name="x0", vtype=GRB.INTEGER)  # hours worked by George
x1 = m.addVar(name="x1")  # hours worked by Bill
x2 = m.addVar(name="x2")  # hours worked by Laura

# Objective function
m.setObjective(8 * x0**2 + 8 * x0 * x1 + 8 * x0 * x2 + 9 * x1**2 + 6 * x1 * x2 + x2**2 + 3 * x0 + 4 * x1 + 5 * x2, GRB.MINIMIZE)

# Constraints
m.addConstr(26 * x0 <= 200)
m.addConstr(5 * x0 <= 138)
m.addConstr(20 * x0 <= 233)
m.addConstr(1 * x0 <= 219)
m.addConstr(3 * x0 <= 198)
m.addConstr(3 * x1 <= 200)
m.addConstr(15 * x1 <= 138)
m.addConstr(24 * x1 <= 233)
m.addConstr(23 * x1 <= 219)
m.addConstr(12 * x1 <= 198)
m.addConstr(22 * x2 <= 200)
m.addConstr(12 * x2 <= 138)
m.addConstr(19 * x2 <= 233)
m.addConstr(29 * x2 <= 219)
m.addConstr(3 * x2 <= 198)
m.addConstr(3 * x1**2 + 22 * x2**2 >= 64)
m.addConstr(26 * x0 + 3 * x1 + 22 * x2 >= 64)
m.addConstr(15 * x1 + 12 * x2 >= 16)
m.addConstr(5 * x0**2 + 12 * x2**2 >= 37)
m.addConstr(5 * x0 + 15 * x1 + 12 * x2 >= 37)
m.addConstr(20 * x0**2 + 19 * x2**2 >= 77)
m.addConstr(20 * x0 + 24 * x1 >= 74)
m.addConstr(20 * x0 + 24 * x1 + 19 * x2 >= 74)
m.addConstr(1 * x0 + 23 * x1 >= 29)
m.addConstr(23 * x1 + 29 * x2 >= 61)
m.addConstr(1 * x0**2 + 23 * x1**2 + 29 * x2**2 >= 72)
m.addConstr(1 * x0 + 23 * x1 + 29 * x2 >= 72)
m.addConstr(3 * x0 + 3 * x2 >= 58)
m.addConstr(12 * x1 + 3 * x2 >= 54)
m.addConstr(3 * x0 + 12 * x1 + 3 * x2 >= 54)
m.addConstr(10 * x0**2 - 8 * x2**2 >= 0)
m.addConstr(9 * x0 - 4 * x1 >= 0)
m.addConstr(26 * x0 + 3 * x1 <= 111)
m.addConstr(5 * x0 + 12 * x2 <= 115)
m.addConstr(12 * x1 + 3 * x2 <= 111)

# Solve the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("x0: ", x0.varValue)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
else:
    print("The model is infeasible")
```