## Step 1: Define the variables and their corresponding coefficients in the objective function
Let's denote the variables as follows:
- $x_0$ = ham sandwiches
- $x_1$ = chicken thighs
- $x_2$ = rotisserie chickens
- $x_3$ = steaks
- $x_4$ = strips of bacon
- $x_5$ = cantaloupes

The objective function to maximize is:
$6.97x_0x_1 + 1.95x_0x_2 + 4.26x_0x_3 + 3.64x_0x_4 + 4.75x_0x_5 + 4.24x_1^2 + 9.26x_1x_2 + 6.36x_2^2 + 4.49x_3^2 + 1.52x_3x_4 + 7.28x_4x_5 + 7.75x_1 + 3.98x_3 + 6.93x_4 + 5.3x_5$

## Step 2: Define the constraints based on the given information
The constraints are:
1. $11x_0 + 10x_1 + 10x_2 + 14x_3 + 6x_4 + 12x_5 \leq 178$ (total grams of protein)
2. $11^2x_0^2 + 10^2x_2^2 \leq 158$ 
3. $10^2x_1^2 + 6^2x_4^2 \leq 152$
4. $6x_4 + 12x_5 \leq 36$
5. $11x_0 + 10x_1 \leq 44$
6. $10x_2 + 12x_5 \leq 53$
7. $11x_0 + 14x_3 \leq 102$
8. $10x_2 + 6x_4 \leq 168$
9. $10^2x_1^2 + 10^2x_2^2 \leq 51$
10. $10x_1 + 14x_3 \leq 118$
11. $10^2x_1^2 + 12^2x_5^2 \leq 171$
12. $11x_0 + 10x_1 + 10x_2 + 14x_3 + 6x_4 + 12x_5 \leq 171$

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

```python
import gurobi as gp

# Define the model
m = gp.Model("optimization_problem")

# Define the variables
x0 = m.addVar(name="ham_sandwiches", lb=0)  # ham sandwiches
x1 = m.addVar(name="chicken_thighs", lb=0)  # chicken thighs
x2 = m.addVar(name="rotisserie_chickens", lb=0)  # rotisserie chickens
x3 = m.addVar(name="steaks", lb=0)  # steaks
x4 = m.addVar(name="strips_of_bacon", lb=0)  # strips of bacon
x5 = m.addVar(name="cantaloupes", lb=0)  # cantaloupes

# Objective function
m.setObjective(6.97*x0*x1 + 1.95*x0*x2 + 4.26*x0*x3 + 3.64*x0*x4 + 4.75*x0*x5 +
               4.24*x1**2 + 9.26*x1*x2 + 6.36*x2**2 + 4.49*x3**2 + 1.52*x3*x4 +
               7.28*x4*x5 + 7.75*x1 + 3.98*x3 + 6.93*x4 + 5.3*x5, gp.GRB.MAXIMIZE)

# Constraints
m.addConstr(11*x0 + 10*x1 + 10*x2 + 14*x3 + 6*x4 + 12*x5 <= 178)
m.addConstr(121*x0**2 + 100*x2**2 <= 158)
m.addConstr(100*x1**2 + 36*x4**2 <= 152)
m.addConstr(6*x4 + 12*x5 <= 36)
m.addConstr(11*x0 + 10*x1 <= 44)
m.addConstr(10*x2 + 12*x5 <= 53)
m.addConstr(11*x0 + 14*x3 <= 102)
m.addConstr(10*x2 + 6*x4 <= 168)
m.addConstr(100*x1**2 + 100*x2**2 <= 51)
m.addConstr(10*x1 + 14*x3 <= 118)
m.addConstr(100*x1**2 + 144*x5**2 <= 171)
m.addConstr(11*x0 + 10*x1 + 10*x2 + 14*x3 + 6*x4 + 12*x5 <= 171)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("ham sandwiches: ", x0.varValue)
    print("chicken thighs: ", x1.varValue)
    print("rotisserie chickens: ", x2.varValue)
    print("steaks: ", x3.varValue)
    print("strips of bacon: ", x4.varValue)
    print("cantaloupes: ", x5.varValue)
else:
    print("The model is infeasible")
```