## Step 1: Define the symbolic representation of the variables
The variables are ['potatoes', 'rotisserie chickens', 'corn cobs'] which can be represented symbolically as ['x1', 'x2', 'x3'].

## Step 2: Convert the natural language description into a symbolic representation
The symbolic representation of the variables is:
- x1: potatoes
- x2: rotisserie chickens
- x3: corn cobs

## Step 3: Render the objective function with symbolic variables
The objective function to maximize is: $6.51x1^2 + 6.3x1x2 + 8.57x2^2 + 3.48x2x3 + 7.18x3^2 + 4.64x2 + 3.49x3$.

## 4: List the constraints with symbolic variables
The constraints are:
- $5.32x1 \leq 5.32$ (healthiness rating of potatoes, but this seems to be an equality or a given parameter, not a constraint in the traditional sense)
- $5.14x2 \leq 5.14$ (healthiness rating of rotisserie chickens, similarly)
- $0.57x3 \leq 0.57$ (healthiness rating of corn cobs)
- $-x2 + 10x3 \geq 0$
- $5.32x1 + 0.57x3 \leq 47$
- $(5.14x2)^2 + (0.57x3)^2 \leq 67$
- $(5.32x1)^2 + (5.14x2)^2 \leq 74$
- $5.32x1 + 5.14x2 + 0.57x3 \leq 74$
- $x1$ is continuous
- $x2$ is integer
- $x3$ is continuous

## 5: Correct and clarify constraints
Correcting and clarifying:
- The healthiness ratings given are not constraints but parameters. Thus, we consider:
- $x2 \in \mathbb{Z}$ (integer constraint)
- $-x2 + 10x3 \geq 0$
- $5.32x1 + 0.57x3 \leq 47$
- $(5.14)^2x2^2 + (0.57)^2x3^2 \leq 67$
- $(5.32)^2x1^2 + (5.14)^2x2^2 \leq 74$
- $5.32x1 + 5.14x2 + 0.57x3 \leq 74$

## 6: Formulate the problem in Gurobi
We will use Gurobi to solve this optimization problem.

```json
{
    'sym_variables': [('x1', 'potatoes'), ('x2', 'rotisserie chickens'), ('x3', 'corn cobs')],
    'objective_function': '6.51x1^2 + 6.3x1x2 + 8.57x2^2 + 3.48x2x3 + 7.18x3^2 + 4.64x2 + 3.49x3',
    'constraints': [
        '-x2 + 10x3 >= 0',
        '5.32x1 + 0.57x3 <= 47',
        '(5.14)^2x2^2 + (0.57)^2x3^2 <= 67',
        '(5.32)^2x1^2 + (5.14)^2x2^2 <= 74',
        '5.32x1 + 5.14x2 + 0.57x3 <= 74'
    ]
}
```

## 7: Write the Gurobi code
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()
    
    # Define variables
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="potatoes", vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="rotisserie_chickens", vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="corn_cobs", vtype=gurobi.GRB.CONTINUOUS)
    
    # Objective function
    model.setObjective(6.51*x1**2 + 6.3*x1*x2 + 8.57*x2**2 + 3.48*x2*x3 + 7.18*x3**2 + 4.64*x2 + 3.49*x3, gurobi.GRB.MAXIMIZE)
    
    # Constraints
    model.addConstr(-x2 + 10*x3 >= 0, name="constraint_1")
    model.addConstr(5.32*x1 + 0.57*x3 <= 47, name="constraint_2")
    model.addConstr((5.14)**2*x2**2 + (0.57)**2*x3**2 <= 67, name="constraint_3")
    model.addConstr((5.32)**2*x1**2 + (5.14)**2*x2**2 <= 74, name="constraint_4")
    model.addConstr(5.32*x1 + 5.14*x2 + 0.57*x3 <= 74, name="constraint_5")
    
    # Optimize
    model.optimize()
    
    # Print solution
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Potatoes: ", x1.varValue)
        print("Rotisserie Chickens: ", x2.varValue)
        print("Corn Cobs: ", x3.varValue)
    else:
        print("No solution found")

solve_optimization_problem()
```