## Step 1: Define the variables and their attributes
We have the following variables: 
- $x_0$: packs of napkins
- $x_1$: lightbulbs
- $x_2$: cookies
- $x_3$: paper towel rolls
- $x_4$: cartons of milk

And their respective attributes are given in the dictionary:
```python
resources = {
    'r0': {'description': 'storage space', 'upper_bound': 121, 'x0': 9, 'x1': 3, 'x2': 11, 'x3': 4, 'x4': 8},
    'r1': {'description': 'weight', 'upper_bound': 154, 'x0': 11, 'x1': 11, 'x2': 2, 'x3': 14, 'x4': 2}
}
```

## Step 2: Formulate the objective function
The objective function to minimize is:
\[ 4x_0^2 + 7x_0x_1 + 2x_0x_2 + 4x_0x_3 + 6x_0x_4 + 3x_1^2 + 7x_1x_2 + 9x_1x_3 + 5x_1x_4 + x_2^2 + 7x_2x_3 + 5x_3^2 + 9x_3x_4 + 6x_4^2 + 2x_0 + 2x_1 + 7x_2 + 9x_3 + 2x_4 \]

## 3: Define the constraints
Constraints based on the problem description:
1. $9x_0 \leq 121$
2. $11x_0 \leq 154$
3. $3x_1 \leq 121$
4. $11x_1 \leq 154$
5. $11x_2 \leq 121$
6. $2x_2 \leq 154$
7. $4x_3 \leq 121$
8. $14x_3 \leq 154$
9. $8x_4 \leq 121$
10. $2x_4 \leq 154$
11. $4x_3 + 8x_4 \geq 13$
12. $9x_0 + 11x_2 \geq 21$
13. $9x_0 + 3x_1 \geq 23$
14. $3x_1 + 4x_3 \geq 11$
15. $3x_1^2 + 2x_4^2 \geq 23$
16. $9x_0 + 4x_3 \geq 15$
17. $9x_0 + 3x_1 + 4x_3 \geq 12$
18. $9x_0 + 3x_1 + 11x_2 + 4x_3 + 8x_4 \geq 12$
19. $11x_0^2 + 11x_1^2 \geq 30$
20. $11x_0^2 + 2x_4^2 \geq 14$
21. $11x_0^2 + 2x_2^2 \geq 16$
22. $11x_1 + 2x_4 \geq 16$
23. $11x_1 + 14x_3 \geq 23$
24. $2x_2 + 2x_4 \geq 27$
25. $2x_2^2 + 5x_3^2 \geq 11$
26. $11x_0 + 14x_3 \geq 23$
27. $11x_0^2 + 11x_1^2 + 2x_4^2 \geq 27$
28. $2x_2 + 14x_3 + 2x_4 \geq 27$
29. $11x_0 + 11x_1 + 2x_4 \geq 22$
30. $2x_2 + 14x_3 + 2x_4 \geq 22$
31. $11x_0 + 11x_1 + 2x_2 + 14x_3 + 2x_4 \geq 22$
32. $-x_1 + 4x_4 \geq 0$
33. $-8x_2 + 8x_4 \geq 0$
34. $3x_1 + 11x_2 \leq 121$
35. $9x_0^2 + 11x_2^2 \leq 37$

## 4: Implement the problem in Gurobi
```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define the variables
x0 = m.addVar(name="packs of napkins", vtype=gurobi.GRB.INTEGER)
x1 = m.addVar(name="lightbulbs", vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name="cookies", vtype=gurobi.GRB.INTEGER)
x3 = m.addVar(name="paper towel rolls", vtype=gurobi.GRB.INTEGER)
x4 = m.addVar(name="cartons of milk", vtype=gurobi.GRB.INTEGER)

# Objective function
m.setObjective(4*x0**2 + 7*x0*x1 + 2*x0*x2 + 4*x0*x3 + 6*x0*x4 + 
               3*x1**2 + 7*x1*x2 + 9*x1*x3 + 5*x1*x4 + x2**2 + 
               7*x2*x3 + 5*x3**2 + 9*x3*x4 + 6*x4**2 + 2*x0 + 
               2*x1 + 7*x2 + 9*x3 + 2*x4, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(9*x0 <= 121)
m.addConstr(11*x0 <= 154)
m.addConstr(3*x1 <= 121)
m.addConstr(11*x1 <= 154)
m.addConstr(11*x2 <= 121)
m.addConstr(2*x2 <= 154)
m.addConstr(4*x3 <= 121)
m.addConstr(14*x3 <= 154)
m.addConstr(8*x4 <= 121)
m.addConstr(2*x4 <= 154)
m.addConstr(4*x3 + 8*x4 >= 13)
m.addConstr(9*x0 + 11*x2 >= 21)
m.addConstr(9*x0 + 3*x1 >= 23)
m.addConstr(3*x1 + 4*x3 >= 11)
m.addConstr(3*x1**2 + 2*x4**2 >= 23)
m.addConstr(9*x0 + 4*x3 >= 15)
m.addConstr(9*x0 + 3*x1 + 4*x3 >= 12)
m.addConstr(9*x0 + 3*x1 + 11*x2 + 4*x3 + 8*x4 >= 12)
m.addConstr(11*x0**2 + 11*x1**2 >= 30)
m.addConstr(11*x0**2 + 2*x4**2 >= 14)
m.addConstr(11*x0**2 + 2*x2**2 >= 16)
m.addConstr(11*x1 + 2*x4 >= 16)
m.addConstr(11*x1 + 14*x3 >= 23)
m.addConstr(2*x2 + 2*x4 >= 27)
m.addConstr(2*x2**2 + 5*x3**2 >= 11)
m.addConstr(11*x0 + 14*x3 >= 23)
m.addConstr(11*x0**2 + 11*x1**2 + 2*x4**2 >= 27)
m.addConstr(2*x2 + 14*x3 + 2*x4 >= 27)
m.addConstr(11*x0 + 11*x1 + 2*x4 >= 22)
m.addConstr(2*x2 + 14*x3 + 2*x4 >= 22)
m.addConstr(11*x0 + 11*x1 + 2*x2 + 14*x3 + 2*x4 >= 22)
m.addConstr(-x1 + 4*x4 >= 0)
m.addConstr(-8*x2 + 8*x4 >= 0)
m.addConstr(3*x1 + 11*x2 <= 121)
m.addConstr(9*x0**2 + 11*x2**2 <= 37)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.Status.OPTIMAL:
    print("Objective: ", m.objVal)
    print("packs of napkins: ", x0.varValue)
    print("lightbulbs: ", x1.varValue)
    print("cookies: ", x2.varValue)
    print("paper towel rolls: ", x3.varValue)
    print("cartons of milk: ", x4.varValue)
else:
    print("No solution found")
```

```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define the variables
x0 = m.addVar(name="packs of napkins", vtype=gurobi.GRB.INTEGER)
x1 = m.addVar(name="lightbulbs", vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name="cookies", vtype=gurobi.GRB.INTEGER)
x3 = m.addVar(name="paper towel rolls", vtype=gurobi.GRB.INTEGER)
x4 = m.addVar(name="cartons of milk", vtype=gurobi.GRB.INTEGER)

# Objective function
m.setObjective(4*x0**2 + 7*x0*x1 + 2*x0*x2 + 4*x0*x3 + 6*x0*x4 + 
               3*x1**2 + 7*x1*x2 + 9*x1*x3 + 5*x1*x4 + x2**2 + 
               7*x2*x3 + 5*x3**2 + 9*x3*x4 + 6*x4**2 + 2*x0 + 
               2*x1 + 7*x2 + 9*x3 + 2*x4, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(9*x0 <= 121)
m.addConstr(11*x0 <= 154)
m.addConstr(3*x1 <= 121)
m.addConstr(11*x1 <= 154)
m.addConstr(11*x2 <= 121)
m.addConstr(2*x2 <= 154)
m.addConstr(4*x3 <= 121)
m.addConstr(14*x3 <= 154)
m.addConstr(8*x4 <= 121)
m.addConstr(2*x4 <= 154)
m.addConstr(4*x3 + 8*x4 >= 13)
m.addConstr(9*x0 + 11*x2 >= 21)
m.addConstr(9*x0 + 3*x1 >= 23)
m.addConstr(3*x1 + 4*x3 >= 11)
m.addConstr(3*x1**2 + 2*x4**2 >= 23)
m.addConstr(9*x0 + 4*x3 >= 15)
m.addConstr(9*x0 + 3*x1 + 4*x3 >= 12)
m.addConstr(9*x0 + 3*x1 + 11*x2 + 4*x3 + 8*x4 >= 12)
m.addConstr(11*x0**2 + 11*x1**2 >= 30)
m.addConstr(11*x0**2 + 2*x4**2 >= 14)
m.addConstr(11*x0**2 + 2*x2**2 >= 16)
m.addConstr(11*x1 + 2*x4 >= 16)
m.addConstr(11*x1 + 14*x3 >= 23)
m.addConstr(2*x2 + 2*x4 >= 27)
m.addConstr(2*x2**2 + 5*x3**2 >= 11)
m.addConstr(11*x0 + 14*x3 >= 23)
m.addConstr(11*x0**2 + 11*x1**2 + 2*x4**2 >= 27)
m.addConstr(2*x2 + 14*x3 + 2*x4 >= 27)
m.addConstr(11*x0 + 11*x1 + 2*x4 >= 22)
m.addConstr(2*x2 + 14*x3 + 2*x4 >= 22)
m.addConstr(11*x0 + 11*x1 + 2*x2 + 14*x3 + 2*x4 >= 22)
m.addConstr(-x1 + 4*x4 >= 0)
m.addConstr(-8*x2 + 8*x4 >= 0)
m.addConstr(3*x1 + 11*x2 <= 121)
m.addConstr(9*x0**2 + 11*x2**2 <= 37)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.Status.OPTIMAL:
    print("Objective: ", m.objVal)
    print("packs of napkins: ", x0.varValue)
    print("lightbulbs: ", x1.varValue)
    print("cookies: ", x2.varValue)
    print("paper towel rolls: ", x3.varValue)
    print("cartons of milk: ", x4.varValue)
else:
    print("No solution found")
```