## Step 1: Define the symbolic representation of the variables
The variables are: ['ham sandwiches', 'chicken thighs', 'rotisserie chickens', 'steaks', 'strips of bacon', 'cantaloupes']. Let's denote them as $x_1, x_2, x_3, x_4, x_5, x_6$ respectively.

## Step 2: Convert the natural language objects into symbolic variables
The symbolic variables are: 
- $x_1$ for 'ham sandwiches'
- $x_2$ for 'chicken thighs'
- $x_3$ for 'rotisserie chickens'
- $x_4$ for 'steaks'
- $x_5$ for 'strips of bacon'
- $x_6$ for 'cantaloupes'

## 3: Define the objective function using symbolic variables
The objective function to maximize is: 
\[ 6.97x_1x_2 + 1.95x_1x_3 + 4.26x_1x_4 + 3.64x_1x_5 + 4.75x_1x_6 + 4.24x_2^2 + 9.26x_2x_3 + 6.36x_3^2 + 4.49x_4^2 + 1.52x_4x_5 + 7.28x_5x_6 + 7.75x_2 + 3.98x_4 + 6.93x_5 + 5.3x_6 \]

## 4: List the constraints
The constraints are:
- $11x_1 + 10x_2 + 10x_3 + 14x_4 + 6x_5 + 12x_6 \leq 178$
- $11^2x_1^2 + 10^2x_3^2 \leq 158$
- $10^2x_2^2 + 6^2x_5^2 \leq 152$
- $6x_5 + 12x_6 \leq 36$
- $11x_1 + 10x_2 \leq 44$
- $10x_3 + 12x_6 \leq 53$
- $11x_1 + 14x_4 \leq 102$
- $10x_3 + 6x_5 \leq 168$
- $10^2x_2^2 + 10^2x_3^2 \leq 51$
- $10x_2 + 14x_4 \leq 118$
- $10^2x_2^2 + 12^2x_6^2 \leq 171$
- $11x_1 + 10x_2 + 10x_3 + 14x_4 + 6x_5 + 12x_6 \leq 171$

## 5: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'ham sandwiches'), 
        ('x2', 'chicken thighs'), 
        ('x3', 'rotisserie chickens'), 
        ('x4', 'steaks'), 
        ('x5', 'strips of bacon'), 
        ('x6', 'cantaloupes')
    ], 
    'objective_function': '6.97*x1*x2 + 1.95*x1*x3 + 4.26*x1*x4 + 3.64*x1*x5 + 4.75*x1*x6 + 4.24*x2^2 + 9.26*x2*x3 + 6.36*x3^2 + 4.49*x4^2 + 1.52*x4*x5 + 7.28*x5*x6 + 7.75*x2 + 3.98*x4 + 6.93*x5 + 5.3*x6', 
    'constraints': [
        '11*x1 + 10*x2 + 10*x3 + 14*x4 + 6*x5 + 12*x6 <= 178',
        '121*x1^2 + 100*x3^2 <= 158',
        '100*x2^2 + 36*x5^2 <= 152',
        '6*x5 + 12*x6 <= 36',
        '11*x1 + 10*x2 <= 44',
        '10*x3 + 12*x6 <= 53',
        '11*x1 + 14*x4 <= 102',
        '10*x3 + 6*x5 <= 168',
        '100*x2^2 + 100*x3^2 <= 51',
        '10*x2 + 14*x4 <= 118',
        '100*x2^2 + 144*x6^2 <= 171',
        '11*x1 + 10*x2 + 10*x3 + 14*x4 + 6*x5 + 12*x6 <= 171'
    ]
}
```

## 6: Implement the optimization problem using Gurobi
```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
x1 = m.addVar(name="ham_sandwiches", lb=0)  # No lower bound specified, assuming 0
x2 = m.addVar(name="chicken_thighs", lb=0)
x3 = m.addVar(name="rotisserie_chickens", lb=0)
x4 = m.addVar(name="steaks", lb=0)
x5 = m.addVar(name="strips_of_bacon", lb=0)
x6 = m.addVar(name="cantaloupes", lb=0)

# Define the objective function
m.setObjective(6.97*x1*x2 + 1.95*x1*x3 + 4.26*x1*x4 + 3.64*x1*x5 + 4.75*x1*x6 + 
               4.24*x2**2 + 9.26*x2*x3 + 6.36*x3**2 + 4.49*x4**2 + 1.52*x4*x5 + 
               7.28*x5*x6 + 7.75*x2 + 3.98*x4 + 6.93*x5 + 5.3*x6, gp.GRB.MAXIMIZE)

# Define the constraints
m.addConstr(11*x1 + 10*x2 + 10*x3 + 14*x4 + 6*x5 + 12*x6 <= 178)
m.addConstr(121*x1**2 + 100*x3**2 <= 158)
m.addConstr(100*x2**2 + 36*x5**2 <= 152)
m.addConstr(6*x5 + 12*x6 <= 36)
m.addConstr(11*x1 + 10*x2 <= 44)
m.addConstr(10*x3 + 12*x6 <= 53)
m.addConstr(11*x1 + 14*x4 <= 102)
m.addConstr(10*x3 + 6*x5 <= 168)
m.addConstr(100*x2**2 + 100*x3**2 <= 51)
m.addConstr(10*x2 + 14*x4 <= 118)
m.addConstr(100*x2**2 + 144*x6**2 <= 171)
m.addConstr(11*x1 + 10*x2 + 10*x3 + 14*x4 + 6*x5 + 12*x6 <= 171)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.Status.OPTIMAL:
    print("Objective: ", m.objVal)
    print("ham sandwiches: ", x1.varValue)
    print("chicken thighs: ", x2.varValue)
    print("rotisserie chickens: ", x3.varValue)
    print("steaks: ", x4.varValue)
    print("strips of bacon: ", x5.varValue)
    print("cantaloupes: ", x6.varValue)
else:
    print("The model is infeasible")
```