## Step 1: Define the optimization problem and its components
The problem requires minimizing an objective function subject to various constraints. The objective function to minimize is: $7.68G^2 + 8.67GB + 3.79B^2 + 6.11BJ + 6.09J^2 + 4.46G + 3.47B + 3.11J$, where $G$, $B$, and $J$ represent the hours worked by George, Bill, and John, respectively.

## 2: List all constraints
The constraints are:
1. $G \geq 0$, $B \geq 0$, $J \geq 0$ (Implicit non-negativity constraints)
2. $1.95G \leq 107$
3. $15.65G \leq 166$
4. $14.78G \leq 146$
5. $8.5G \leq 163$
6. $3.2B \leq 107$
7. $1.68B \leq 166$
8. $0.75B \leq 146$
9. $10.83B \leq 163$
10. $5.58J \leq 107$
11. $10.13J \leq 166$
12. $5.11J \leq 146$
13. $14.06J \leq 163$
14. $3.2B + 5.58J \geq 26$
15. $1.95G + 3.2B + 5.58J \geq 26$
16. $15.65G^2 + 10.13J^2 \geq 33$
17. $15.65G + 1.68B \geq 34$
18. $15.65G + 1.68B + 10.13J \geq 34$
19. $14.78G + 0.75B \geq 33$
20. $0.75B + 5.11J \geq 32$
21. $14.78G + 0.75B + 5.11J \geq 32$
22. $8.5G + 14.06J \geq 25$
23. $10.83B + 14.06J \geq 29$
24. $8.5G + 10.83B + 14.06J \geq 29$
25. $10B - 7J \geq 0$
26. $9G - 9B \geq 0$
27. $1.95G + 3.2B \leq 36$
28. $1.68B + 10.13J \leq 119$
29. $8.5G^2 + 10.83B^2 \leq 71$
30. $8.5G + 10.83B + 14.06J \leq 162$
31. $G$ must be an integer
32. $B$ can be any real number
33. $J$ can be any real number

## 3: Convert the problem into Gurobi code
```python
import gurobi as gp

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

# Define variables
G = m.addVar(lb=0, name="hours_worked_by_George", vtype=gp.GRB.INTEGER)
B = m.addVar(lb=0, name="hours_worked_by_Bill")
J = m.addVar(lb=0, name="hours_worked_by_John")

# Objective function
m.setObjective(7.68*G**2 + 8.67*G*B + 3.79*B**2 + 6.11*B*J + 6.09*J**2 + 4.46*G + 3.47*B + 3.11*J, gp.GRB.MINIMIZE)

# Constraints
m.addConstr(1.95*G <= 107)
m.addConstr(15.65*G <= 166)
m.addConstr(14.78*G <= 146)
m.addConstr(8.5*G <= 163)
m.addConstr(3.2*B <= 107)
m.addConstr(1.68*B <= 166)
m.addConstr(0.75*B <= 146)
m.addConstr(10.83*B <= 163)
m.addConstr(5.58*J <= 107)
m.addConstr(10.13*J <= 166)
m.addConstr(5.11*J <= 146)
m.addConstr(14.06*J <= 163)
m.addConstr(3.2*B + 5.58*J >= 26)
m.addConstr(1.95*G + 3.2*B + 5.58*J >= 26)
m.addConstr(15.65*G**2 + 10.13*J**2 >= 33)
m.addConstr(15.65*G + 1.68*B >= 34)
m.addConstr(15.65*G + 1.68*B + 10.13*J >= 34)
m.addConstr(14.78*G + 0.75*B >= 33)
m.addConstr(0.75*B + 5.11*J >= 32)
m.addConstr(14.78*G + 0.75*B + 5.11*J >= 32)
m.addConstr(8.5*G + 14.06*J >= 25)
m.addConstr(10.83*B + 14.06*J >= 29)
m.addConstr(8.5*G + 10.83*B + 14.06*J >= 29)
m.addConstr(10*B - 7*J >= 0)
m.addConstr(9*G - 9*B >= 0)
m.addConstr(1.95*G + 3.2*B <= 36)
m.addConstr(1.68*B + 10.13*J <= 119)
m.addConstr(8.5*G**2 + 10.83*B**2 <= 71)
m.addConstr(8.5*G + 10.83*B + 14.06*J <= 162)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Hours worked by George: ", G.varValue)
    print("Hours worked by Bill: ", B.varValue)
    print("Hours worked by John: ", J.varValue)
else:
    print("The model is infeasible")
```