## Problem Description and Formulation

The problem is an optimization problem with the goal to maximize an objective function subject to several constraints. The variables are 'kiwis', 'eggs', and 'cherry pies'. The objective function to maximize is:

\[ 3 \times \text{kiwis} \times \text{eggs} + 2 \times \text{kiwis} + 4 \times \text{eggs} \]

Subject to constraints on healthiness rating, milligrams of iron, and grams of carbohydrates.

## Constraints

1. Healthiness rating constraints:
   - \(11 \times \text{kiwis} + 6 \times \text{eggs} \leq 172\)
   - \(11 \times \text{kiwis} + 3 \times \text{cherry pies} \leq 141\)
   - \(11 \times \text{kiwis} + 6 \times \text{eggs} + 3 \times \text{cherry pies} \leq 141\)

2. Milligrams of iron constraints:
   - \(5 \times \text{eggs} + 7 \times \text{cherry pies} \leq 82\)
   - \((\text{kiwis})^2 + (\text{eggs})^2 \leq 83\)
   - \(\text{kiwis} + \text{eggs} + \text{cherry pies} \leq 83\)

3. Grams of carbohydrates constraints:
   - \((\text{kiwis})^2 + (\text{eggs})^2 \leq 84\)
   - \((\text{kiwis})^2 + (\text{eggs})^2 + (\text{cherry pies})^2 \leq 175\)
   - \(\text{kiwis} + \text{eggs} + \text{cherry pies} \leq 175\)

## Gurobi Code

```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    kiwis = model.addVar(lb=0, name="kiwis", vtype=gurobi.GRB.CONTINUOUS)
    eggs = model.addVar(lb=0, name="eggs", vtype=gurobi.GRB.CONTINUOUS)
    cherry_pies = model.addVar(lb=0, name="cherry_pies", vtype=gurobi.GRB.CONTINUOUS)

    # Objective function
    model.setObjective(3 * kiwis * eggs + 2 * kiwis + 4 * eggs, gurobi.GRB.MAXIMIZE)

    # Healthiness rating constraints
    model.addConstr(11 * kiwis + 6 * eggs <= 172, name="healthiness_kiwis_eggs")
    model.addConstr(11 * kiwis + 3 * cherry_pies <= 141, name="healthiness_kiwis_pies")
    model.addConstr(11 * kiwis + 6 * eggs + 3 * cherry_pies <= 141, name="healthiness_all")

    # Milligrams of iron constraints
    model.addConstr(5 * eggs + 7 * cherry_pies <= 82, name="iron_eggs_pies")
    model.addConstr(kiwis**2 + eggs**2 <= 83, name="iron_kiwis_eggs_squared")
    model.addConstr(kiwis + eggs + cherry_pies <= 83, name="iron_all")

    # Grams of carbohydrates constraints
    model.addConstr(kiwis**2 + eggs**2 <= 84, name="carbohydrates_kiwis_eggs_squared")
    model.addConstr(kiwis**2 + eggs**2 + cherry_pies**2 <= 175, name="carbohydrates_all_squared")
    model.addConstr(kiwis + eggs + cherry_pies <= 175, name="carbohydrates_all")

    # Parameters for resources
    model.addConstr(kiwis * 11 <= 187, name="r0_kiwis")
    model.addConstr(eggs * 6 <= 187, name="r0_eggs")
    model.addConstr(cherry_pies * 3 <= 187, name="r0_pies")

    model.addConstr(kiwis * 1 <= 111, name="r1_kiwis")
    model.addConstr(eggs * 5 <= 111, name="r1_eggs")
    model.addConstr(cherry_pies * 7 <= 111, name="r1_pies")

    model.addConstr(kiwis * 4 <= 195, name="r2_kiwis")
    model.addConstr(eggs * 9 <= 195, name="r2_eggs")
    model.addConstr(cherry_pies * 3 <= 195, name="r2_pies")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Kiwis: ", kiwis.varValue)
        print("Eggs: ", eggs.varValue)
        print("Cherry Pies: ", cherry_pies.varValue)
    else:
        print("No optimal solution found")

solve_optimization_problem()
```