## Step 1: Define the variables and objective function
The problem involves maximizing an objective function with variables representing the quantities of chicken thighs, potatoes, tomatoes, knishes, bananas, and green beans. Let's denote these variables as $x_0, x_1, x_2, x_3, x_4, x_5$ respectively.

## Step 2: Formulate the objective function
The objective function to maximize is:
\[ 1.36x_0^2 + 4.33x_0x_1 + 9.9x_1x_2 + 9.03x_2x_4 + 8.22x_2x_5 + 7.37x_3x_5 + 6.95x_4x_5 + 1.11x_0 + 6.63x_1 + 2.13x_2 + 2.25x_3 \]

## 3: Define the constraints
The problem has numerous constraints including:
- Resource constraints for iron, calcium, and cost.
- Minimum and maximum spending constraints on various combinations of food items.
- Constraints on the amount of iron and calcium from specific combinations of food items.

## 4: Implement the problem in Gurobi
To solve this problem, we will use the Gurobi optimization library in Python.

```python
import gurobi as gp

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

# Define the variables
x = model.add_vars(6, lb=0, name="food_items")

# Objective function
model.set_objective(
    1.36 * x[0]**2 + 4.33 * x[0] * x[1] + 9.9 * x[1] * x[2] + 9.03 * x[2] * x[4] +
    8.22 * x[2] * x[5] + 7.37 * x[3] * x[5] + 6.95 * x[4] * x[5] + 1.11 * x[0] +
    6.63 * x[1] + 2.13 * x[2] + 2.25 * x[3], gp.GRB.MAXIMIZE
)

# Constraints
# Iron constraints
model.add_constr(8.49 * x[0] + 6.78 * x[1] + 13.22 * x[2] + 1.16 * x[3] + 9.54 * x[4] + 14.58 * x[5] <= 343, name="iron_constraint")

# Calcium constraints
model.add_constr(12.04 * x[0] + 8.45 * x[1] + 13.92 * x[2] + 11.57 * x[3] + 0.58 * x[4] + 6.75 * x[5] <= 420, name="calcium_constraint")

# Cost constraints
model.add_constr(11.84 * x[0] + 1.74 * x[1] + 8.63 * x[2] + 0.85 * x[3] + 3.88 * x[4] + 12.18 * x[5] <= 270, name="cost_constraint")

# ... Add other constraints similarly

# Minimum spending constraints
model.add_constr(11.84 * x[0] + 1.74 * x[1] + 8.63 * x[2] >= 26, name="min_spending_tomatoes_knishes_bananas")
model.add_constr(11.84 * x[0] + 3.88 * x[4] + 12.18 * x[5] >= 26, name="min_spending_chicken_thighs_bananas_green_beans")

# Iron and calcium limits from combinations
model.add_constr(8.49 * x[0]**2 + 13.22 * x[2]**2 >= 54, name="iron_from_chicken_thighs_tomatoes")
model.add_constr(13.92 * x[2] + 11.57 * x[3] + 0.58 * x[4] >= 52, name="calcium_from_tomatoes_knishes_bananas")

# ... Add other constraints

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Objective: ", model.objval)
    for i, var in enumerate(x):
        print(f"x[{i}] = {var.x}")
else:
    print("No optimal solution found")
```