To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints in terms of these variables.

Let's denote:
- $x_0$ as the number of bagged salads,
- $x_1$ as the quantity of kiwis,
- $x_2$ as the quantity of strips of bacon.

The objective function to maximize is given by:
\[5.76(x_0)^2 + 7.22(x_1)(x_2) + 7.84(x_2)^2 + 2.36(x_2)\]

Constraints based on iron content and other conditions are as follows:

1. Iron from bagged salads: $20x_0$
2. Iron from kiwis: $18x_1$
3. Iron from strips of bacon: $7x_2$
4. At least 62 milligrams of iron must come from kiwis squared plus strips of bacon squared: $(x_1)^2 + (x_2)^2 \geq \frac{62}{1}$, since the problem doesn't specify the iron content per unit square, we assume it's directly related to the quantity squared.
5. At least 99 milligrams of iron from bagged salads and strips of bacon: $20x_0 + 7x_2 \geq 99$
6. No more than 221 milligrams of iron from kiwis squared and strips of bacon squared: $(x_1)^2 + (x_2)^2 \leq \frac{221}{1}$
7. No more than 203 milligrams of iron from bagged salads squared plus strips of bacon squared: $(x_0)^2 + (x_2)^2 \leq \frac{203}{1}$
8. At most 203 milligrams of iron can come from the sum of bagged salads, kiwis, and strips of bacon: $20x_0 + 18x_1 + 7x_2 \leq 203$

Symbolic representation:
```json
{
  'sym_variables': [('x0', 'bagged salads'), ('x1', 'kiwis'), ('x2', 'strips of bacon')],
  'objective_function': '5.76*(x0)**2 + 7.22*x1*x2 + 7.84*(x2)**2 + 2.36*x2',
  'constraints': [
    '(x1)**2 + (x2)**2 >= 62',
    '20*x0 + 7*x2 >= 99',
    '(x1)**2 + (x2)**2 <= 221',
    '(x0)**2 + (x2)**2 <= 203',
    '20*x0 + 18*x1 + 7*x2 <= 203'
  ]
}
```

Given the complexity of the constraints and the objective function, solving this problem directly requires numerical methods. Here's how you could implement it in Gurobi using Python:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define variables
x0 = m.addVar(name='bagged_salads', lb=-GRB.INFINITY, ub=GRB.INFINITY)
x1 = m.addVar(name='kiwis', lb=-GRB.INFINITY, ub=GRB.INFINITY)
x2 = m.addVar(name='strips_of_bacon', lb=-GRB.INFINITY, ub=GRB.INFINITY)

# Objective function
m.setObjective(5.76*x0**2 + 7.22*x1*x2 + 7.84*x2**2 + 2.36*x2, GRB.MAXIMIZE)

# Constraints
m.addConstr(x1**2 + x2**2 >= 62)
m.addConstr(20*x0 + 7*x2 >= 99)
m.addConstr(x1**2 + x2**2 <= 221)
m.addConstr(x0**2 + x2**2 <= 203)
m.addConstr(20*x0 + 18*x1 + 7*x2 <= 203)

# Solve the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Bagged salads: {x0.x}")
    print(f"Kiwis: {x1.x}")
    print(f"Strips of bacon: {x2.x}")
else:
    print("No optimal solution found.")
```