## Step 1: Define the optimization problem
The problem is to minimize the objective function: $8.78 \times \text{cheeseburgers} + 9.72 \times \text{cantaloupes} + 6.84 \times \text{protein bars} + 3.94 \times \text{blueberry pies}$.

## Step 2: List all the constraints
1. $\text{cheeseburgers} \times 12 + \text{cantaloupes} \times 1 + \text{protein bars} \times 11 + \text{blueberry pies} \times 12 \leq 249$
2. $\text{cheeseburgers} \times 6 + \text{cantaloupes} \times 12 + \text{protein bars} \times 8 + \text{blueberry pies} \times 8 \leq 231$
3. $\text{cheeseburgers} \times 2 + \text{cantaloupes} \times 2 + \text{protein bars} \times 3 + \text{blueberry pies} \times 16 \leq 98$
4. $\text{cantaloupes} \times 1 + \text{protein bars} \times 11 \geq 32$
5. $\text{cantaloupes} \times 1 + \text{blueberry pies} \times 12 \geq 36$
6. $\text{cheeseburgers} \times 12 + \text{cantaloupes} \times 1 \geq 55$
7. $\text{cheeseburgers} \times 12 + \text{cantaloupes} \times 1 + \text{protein bars} \times 11 + \text{blueberry pies} \times 12 \geq 55$
8. $\text{cheeseburgers} \times 6 + \text{cantaloupes} \times 12 \geq 57$
9. $\text{protein bars} \times 8 + \text{blueberry pies} \times 8 \geq 42$
10. $\text{cheeseburgers} \times 6 + \text{protein bars} \times 8 \geq 29$
11. $\text{cheeseburgers} \times 6 + \text{cantaloupes} \times 12 + \text{protein bars} \times 8 \geq 54$
12. $\text{cheeseburgers} \times 6 + \text{cantaloupes} \times 12 + \text{protein bars} \times 8 + \text{blueberry pies} \times 8 \geq 54$
13. $\text{protein bars} \times 3 + \text{blueberry pies} \times 16 \geq 20$
14. $\text{cantaloupes} \times 2 + \text{protein bars} \times 3 \geq 10$
15. $\text{cantaloupes} \times 2 + \text{blueberry pies} \times 16 \geq 24$
16. $\text{cheeseburgers} \times 2 + \text{cantaloupes} \times 2 + \text{protein bars} \times 3 + \text{blueberry pies} \times 16 \geq 24$
17. $-9 \times \text{cantaloupes} + 10 \times \text{blueberry pies} \geq 0$
18. $6 \times \text{cheeseburgers} - 5 \times \text{protein bars} \geq 0$
19. $-9 \times \text{cheeseburgers} + 7 \times \text{blueberry pies} \geq 0$
20. $\text{cheeseburgers} \times 12 + \text{blueberry pies} \times 12 \leq 117$
21. $\text{protein bars} \times 11 + \text{blueberry pies} \times 12 \leq 181$
22. $\text{cantaloupes} \times 1 + \text{protein bars} \times 11 + \text{blueberry pies} \times 12 \leq 69$
23. $\text{cheeseburgers} \times 12 + \text{cantaloupes} \times 1 + \text{protein bars} \times 11 \leq 64$
24. $\text{cheeseburgers} \times 6 + \text{cantaloupes} \times 12 + \text{protein bars} \times 8 \leq 230$
25. $\text{cheeseburgers} \times 2 + \text{protein bars} \times 3 \leq 82$
26. $\text{protein bars} \times 3 + \text{blueberry pies} \times 16 \leq 39$

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

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

# Define the variables
cheeseburgers = m.addVar(name="cheeseburgers", lb=0)
cantaloupes = m.addVar(name="cantaloupes", lb=0)
protein_bars = m.addVar(name="protein_bars", lb=0)
blueberry_pies = m.addVar(name="blueberry_pies", lb=0)

# Define the objective function
m.setObjective(8.78 * cheeseburgers + 9.72 * cantaloupes + 6.84 * protein_bars + 3.94 * blueberry_pies, gurobi.GRB.MINIMIZE)

# Add constraints
m.addConstr(12 * cheeseburgers + cantaloupes + 11 * protein_bars + 12 * blueberry_pies <= 249)
m.addConstr(6 * cheeseburgers + 12 * cantaloupes + 8 * protein_bars + 8 * blueberry_pies <= 231)
m.addConstr(2 * cheeseburgers + 2 * cantaloupes + 3 * protein_bars + 16 * blueberry_pies <= 98)
m.addConstr(cantaloupes + 11 * protein_bars >= 32)
m.addConstr(cantaloupes + 12 * blueberry_pies >= 36)
m.addConstr(12 * cheeseburgers + cantaloupes >= 55)
m.addConstr(12 * cheeseburgers + cantaloupes + 11 * protein_bars + 12 * blueberry_pies >= 55)
m.addConstr(6 * cheeseburgers + 12 * cantaloupes >= 57)
m.addConstr(8 * protein_bars + 8 * blueberry_pies >= 42)
m.addConstr(6 * cheeseburgers + 8 * protein_bars >= 29)
m.addConstr(6 * cheeseburgers + 12 * cantaloupes + 8 * protein_bars >= 54)
m.addConstr(6 * cheeseburgers + 12 * cantaloupes + 8 * protein_bars + 8 * blueberry_pies >= 54)
m.addConstr(3 * protein_bars + 16 * blueberry_pies >= 20)
m.addConstr(2 * cantaloupes + 3 * protein_bars >= 10)
m.addConstr(2 * cantaloupes + 16 * blueberry_pies >= 24)
m.addConstr(2 * cheeseburgers + 2 * cantaloupes + 3 * protein_bars + 16 * blueberry_pies >= 24)
m.addConstr(-9 * cantaloupes + 10 * blueberry_pies >= 0)
m.addConstr(6 * cheeseburgers - 5 * protein_bars >= 0)
m.addConstr(-9 * cheeseburgers + 7 * blueberry_pies >= 0)
m.addConstr(12 * cheeseburgers + 12 * blueberry_pies <= 117)
m.addConstr(11 * protein_bars + 12 * blueberry_pies <= 181)
m.addConstr(cantaloupes + 11 * protein_bars + 12 * blueberry_pies <= 69)
m.addConstr(12 * cheeseburgers + cantaloupes + 11 * protein_bars <= 64)
m.addConstr(6 * cheeseburgers + 12 * cantaloupes + 8 * protein_bars <= 230)
m.addConstr(2 * cheeseburgers + 3 * protein_bars <= 82)
m.addConstr(3 * protein_bars + 16 * blueberry_pies <= 39)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objval)
    print("Cheeseburgers: ", cheeseburgers.varValue)
    print("Cantaloupes: ", cantaloupes.varValue)
    print("Protein Bars: ", protein_bars.varValue)
    print("Blueberry Pies: ", blueberry_pies.varValue)
else:
    print("The model is infeasible")
```