## Step 1: Define the symbolic representation of the problem
First, let's define the symbolic variables and the objective function based on the given problem description.

## Step 2: Identify the variables and their corresponding symbolic representations
The variables are 'eggs', 'chicken breasts', and 'rotisserie chickens', which we can represent symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## 3: Translate the objective function into symbolic notation
The objective function to minimize is $4.49x_0^2 + 3.26x_1^2 + 6.01x_1x_2 + 6.69x_1 + 3.59x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
1. $4.18x_0$ (healthiness rating of eggs, but this is a given attribute, not a constraint)
2. $6.87x_0$ (milligrams of iron in eggs, but this is a given attribute, not a constraint)
3. $6.74x_1$ (healthiness rating of chicken breasts, but this is a given attribute, not a constraint)
4. $0.06x_1$ (milligrams of iron in chicken breasts, but this is a given attribute, not a constraint)
5. $5.11x_2$ (healthiness rating of rotisserie chickens, but this is a given attribute, not a constraint)
6. $3.0x_2$ (milligrams of iron in rotisserie chickens, but this is a given attribute, not a constraint)
7. $6.74x_1 + 5.11x_2 \geq 24$ (total healthiness rating from chicken breasts and rotisserie chickens)
8. $4.18x_0 + 6.74x_1 + 5.11x_2 \geq 24$ (total healthiness rating from all)
9. $0.06x_1 + 3.0x_2 \geq 30$ (total iron from chicken breasts and rotisserie chickens)
10. $6.87x_0 + 3.0x_2 \geq 24$ (total iron from eggs and rotisserie chickens)
11. $6.87x_0 + 0.06x_1 + 3.0x_2 \geq 24$ (total iron from all)
12. $-10x_1 + 5x_2 \geq 0$ (relationship between chicken breasts and rotisserie chickens)
13. $5x_0^2 - 9x_2^2 \geq 0$ (relationship between eggs and rotisserie chickens)
14. $4.18x_0 + 6.74x_1 \leq 91$ (total healthiness rating from eggs and chicken breasts)
15. $6.74^2x_1^2 + 5.11^2x_2^2 \leq 77$ (total healthiness rating squared from chicken breasts and rotisserie chickens)
16. $0.06x_1 + 3.0x_2 \leq 64$ (total iron from chicken breasts and rotisserie chickens)

## 5: Create the symbolic representation
The symbolic representation is:
```json
{
'sym_variables': [('x0', 'eggs'), ('x1', 'chicken breasts'), ('x2', 'rotisserie chickens')],
'objective_function': '4.49*x0^2 + 3.26*x1^2 + 6.01*x1*x2 + 6.69*x1 + 3.59*x2',
'constraints': [
'6.74*x1 + 5.11*x2 >= 24',
'4.18*x0 + 6.74*x1 + 5.11*x2 >= 24',
'0.06*x1 + 3.0*x2 >= 30',
'6.87*x0 + 3.0*x2 >= 24',
'6.87*x0 + 0.06*x1 + 3.0*x2 >= 24',
'-10*x1 + 5*x2 >= 0',
'5*x0^2 - 9*x2^2 >= 0',
'4.18*x0 + 6.74*x1 <= 91',
'6.74^2*x1^2 + 5.11^2*x2^2 <= 77',
'0.06*x1 + 3.0*x2 <= 64'
]
}
```

## 6: Implement the optimization problem using Gurobi
Now, let's implement this problem using Gurobi in Python.

```python
import gurobi

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

# Define the variables
x0 = model.addVar(name="eggs", lb=-gurobi.GRB.INFINITY)
x1 = model.addVar(name="chicken breasts", lb=-gurobi.GRB.INFINITY)
x2 = model.addVar(name="rotisserie chickens", lb=-gurobi.GRB.INFINITY)

# Define the objective function
model.setObjective(4.49*x0**2 + 3.26*x1**2 + 6.01*x1*x2 + 6.69*x1 + 3.59*x2, gurobi.GRB.MINIMIZE)

# Add constraints
model.addConstr(6.74*x1 + 5.11*x2 >= 24)
model.addConstr(4.18*x0 + 6.74*x1 + 5.11*x2 >= 24)
model.addConstr(0.06*x1 + 3.0*x2 >= 30)
model.addConstr(6.87*x0 + 3.0*x2 >= 24)
model.addConstr(6.87*x0 + 0.06*x1 + 3.0*x2 >= 24)
model.addConstr(-10*x1 + 5*x2 >= 0)
model.addConstr(5*x0**2 - 9*x2**2 >= 0)
model.addConstr(4.18*x0 + 6.74*x1 <= 91)
model.addConstr((6.74*x1)**2 + (5.11*x2)**2 <= 77)
model.addConstr(0.06*x1 + 3.0*x2 <= 64)

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objval)
    print("Eggs: ", x0.varValue)
    print("Chicken Breasts: ", x1.varValue)
    print("Rotisserie Chickens: ", x2.varValue)
else:
    print("The model is infeasible")
```