## Step 1: Define the symbolic representation of the problem
The problem involves minimizing an objective function subject to several constraints. The variables are:
- $x_0$: hours worked by George
- $x_1$: hours worked by Laura
- $x_2$: hours worked by John
- $x_3$: hours worked by Ringo
- $x_4$: hours worked by Peggy

The objective function to minimize is:
\[ 7.9x_0^2 + 5.04x_0x_1 + 2.32x_0x_3 + 9.75x_0x_4 + 5.15x_1x_3 + 7.88x_1x_4 + 8.43x_2^2 + 8.85x_2x_4 + 3.52x_3^2 + 9.29x_3x_4 + 5.95x_4^2 + 2.83x_0 + 3.33x_2 \]

## Step 2: List the constraints
The constraints are:
1. $2.67x_0 \leq 212$
2. $1.45x_0 \leq 39$
3. $2.15x_1 \leq 212$
4. $1.92x_1 \leq 39$
5. $3.94x_2 \leq 212$
6. $1.38x_2 \leq 39$
7. $5.65x_3 \leq 212$
8. $1.87x_3 \leq 39$
9. $2.63x_4 \leq 212$
10. $2.6x_4 \leq 39$
11. $2.15x_1 + 3.94x_2 \geq 40$
12. $2.67^2x_0^2 + 2.15^2x_1^2 \geq 29$
13. $5.65x_3 + 3.94x_2 + 2.15x_1 \geq 33$
14. $2.67x_0 + 2.15x_1 + 3.94x_2 + 5.65x_3 + 2.63x_4 \geq 33$
15. $1.87x_3 + 2.6x_4 \geq 7$
16. $1.92x_1 + 1.87x_3 \geq 4$
17. $1.38x_2 + 1.87x_3 \geq 5$
18. $1.45x_0 + 1.87x_3 \geq 6$
19. $2.6x_4 + 1.45x_0 \geq 5$
20. $1.92x_1 + 1.38x_2 \geq 2$
21. $1.45x_0 + 1.38x_2 \geq 2$
22. $1.45^2x_0^2 + 1.92^2x_1^2 + 1.87^2x_3^2 \geq 4$
23. $1.45x_0 + 1.38x_2 + 1.87x_3 \geq 4$
24. $1.38^2x_2^2 + 1.87^2x_3^2 + 2.6^2x_4^2 \geq 4$
25. $1.92^2x_1^2 + 1.87^2x_3^2 + 2.6^2x_4^2 \geq 4$
26. $1.45x_0 + 1.38x_2 + 2.6x_4 \geq 4$
27. $1.92x_1 + 1.38x_2 + 2.6x_4 \geq 4$
28. $1.45^2x_0^2 + 1.92^2x_1^2 + 2.6^2x_4^2 \geq 4$
29. $1.45x_0 + 1.92x_1 + 1.87x_3 \geq 3$
30. $1.45x_0 + 1.38x_2 + 1.87x_3 \geq 3$
31. $1.87x_3 + 2.6x_4 + 1.38x_2 \geq 3$
32. $1.92^2x_1^2 + 1.87^2x_3^2 + 2.6^2x_4^2 \geq 3$
33. $1.45^2x_0^2 + 1.38^2x_2^2 + 2.6^2x_4^2 \geq 3$
34. $1.92^2x_1^2 + 1.38^2x_2^2 + 1.87^2x_3^2 \geq 3$
35. $1.45^2x_0^2 + 1.92^2x_1^2 + 1.38^2x_2^2 \geq 3$
36. $1.92^2x_1^2 + 1.38^2x_2^2 + 2.6^2x_4^2 \geq 3$
37. $1.45x_0 + 1.92x_1 + 1.87x_3 \geq 6$
38. $1.45x_0 + 1.38x_2 + 1.87x_3 \geq 6$
39. $1.87x_3 + 2.6x_4 + 1.38x_2 \geq 6$
40. $1.45x_0 + 1.92x_1 + 1.38x_2 \geq 6$
41. $8x_3^2 - 3x_4^2 \geq 0$
42. $2.67x_0 + 2.63x_4 \leq 105$
43. $5.65x_3 + 2.63x_4 \leq 74$
44. $5.65^2x_3^2 + 3.94^2x_2^2 + 2.63^2x_4^2 \leq 87$
45. $1.45x_0 + 1.92x_1 \leq 27$

## Step 3: Implement the problem in Gurobi
```python
import gurobi

def optimize_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name="x0", lb=0)  # hours worked by George
    x1 = model.addVar(name="x1", lb=0)  # hours worked by Laura
    x2 = model.addVar(name="x2", lb=0)  # hours worked by John
    x3 = model.addVar(name="x3", lb=0)  # hours worked by Ringo
    x4 = model.addVar(name="x4", lb=0)  # hours worked by Peggy

    # Objective function
    model.setObjective(7.9 * x0**2 + 5.04 * x0 * x1 + 2.32 * x0 * x3 + 9.75 * x0 * x4 +
                       5.15 * x1 * x3 + 7.88 * x1 * x4 + 8.43 * x2**2 + 8.85 * x2 * x4 +
                       3.52 * x3**2 + 9.29 * x3 * x4 + 5.95 * x4**2 + 2.83 * x0 + 3.33 * x2,
                       gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(2.67 * x0 <= 212)
    model.addConstr(1.45 * x0 <= 39)
    model.addConstr(2.15 * x1 <= 212)
    model.addConstr(1.92 * x1 <= 39)
    model.addConstr(3.94 * x2 <= 212)
    model.addConstr(1.38 * x2 <= 39)
    model.addConstr(5.65 * x3 <= 212)
    model.addConstr(1.87 * x3 <= 39)
    model.addConstr(2.63 * x4 <= 212)
    model.addConstr(2.6 * x4 <= 39)
    model.addConstr(2.15 * x1 + 3.94 * x2 >= 40)
    model.addConstr(2.67**2 * x0**2 + 2.15**2 * x1**2 >= 29)
    model.addConstr(5.65 * x3 + 3.94 * x2 + 2.15 * x1 >= 33)
    model.addConstr(2.67 * x0 + 2.15 * x1 + 3.94 * x2 + 5.65 * x3 + 2.63 * x4 >= 33)
    model.addConstr(1.87 * x3 + 2.6 * x4 >= 7)
    model.addConstr(1.92 * x1 + 1.87 * x3 >= 4)
    model.addConstr(1.38 * x2 + 1.87 * x3 >= 5)
    model.addConstr(1.45 * x0 + 1.87 * x3 >= 6)
    model.addConstr(2.6 * x4 + 1.45 * x0 >= 5)
    model.addConstr(1.92 * x1 + 1.38 * x2 >= 2)
    model.addConstr(1.45 * x0 + 1.38 * x2 >= 2)
    model.addConstr(1.45**2 * x0**2 + 1.92**2 * x1**2 + 1.87**2 * x3**2 >= 4)
    model.addConstr(1.45 * x0 + 1.38 * x2 + 1.87 * x3 >= 4)
    model.addConstr(1.38**2 * x2**2 + 1.87**2 * x3**2 + 2.6**2 * x4**2 >= 4)
    model.addConstr(1.92**2 * x1**2 + 1.87**2 * x3**2 + 2.6**2 * x4**2 >= 4)
    model.addConstr(1.45 * x0 + 1.38 * x2 + 2.6 * x4 >= 4)
    model.addConstr(1.92 * x1 + 1.38 * x2 + 2.6 * x4 >= 4)
    model.addConstr(1.45**2 * x0**2 + 1.92**2 * x1**2 + 2.6**2 * x4**2 >= 4)
    model.addConstr(1.45 * x0 + 1.92 * x1 + 1.87 * x3 >= 3)
    model.addConstr(1.45 * x0 + 1.38 * x2 + 1.87 * x3 >= 3)
    model.addConstr(1.87 * x3 + 2.6 * x4 + 1.38 * x2 >= 3)
    model.addConstr(1.92**2 * x1**2 + 1.87**2 * x3**2 + 2.6**2 * x4**2 >= 3)
    model.addConstr(1.45**2 * x0**2 + 1.38**2 * x2**2 + 2.6**2 * x4**2 >= 3)
    model.addConstr(1.92**2 * x1**2 + 1.38**2 * x2**2 + 1.87**2 * x3**2 >= 3)
    model.addConstr(1.45**2 * x0**2 + 1.92**2 * x1**2 + 1.38**2 * x2**2 >= 3)
    model.addConstr(1.92**2 * x1**2 + 1.38**2 * x2**2 + 2.6**2 * x4**2 >= 3)
    model.addConstr(1.45 * x0 + 1.92 * x1 + 1.87 * x3 >= 6)
    model.addConstr(1.45 * x0 + 1.38 * x2 + 1.87 * x3 >= 6)
    model.addConstr(1.87 * x3 + 2.6 * x4 + 1.38 * x2 >= 6)
    model.addConstr(1.45 * x0 + 1.92 * x1 + 1.38 * x2 >= 6)
    model.addConstr(8 * x3**2 - 3 * x4**2 >= 0)
    model.addConstr(2.67 * x0 + 2.63 * x4 <= 105)
    model.addConstr(5.65 * x3 + 2.63 * x4 <= 74)
    model.addConstr(5.65**2 * x3**2 + 3.94**2 * x2**2 + 2.63**2 * x4**2 <= 87)
    model.addConstr(1.45 * x0 + 1.92 * x1 <= 27)

    model.optimize()

    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Optimal solution found.")
        print("Objective: ", model.objVal)
        print("x0: ", x0.varValue)
        print("x1: ", x1.varValue)
        print("x2: ", x2.varValue)
        print("x3: ", x3.varValue)
        print("x4: ", x4.varValue)
    else:
        print("No optimal solution found.")

optimize_problem()
```