## Step 1: Define the optimization problem
The problem is to minimize the objective function: $6.91x_0^2 + 9.46x_0x_1 + 8.04x_2^2 + 1.53x_1 + 2.22x_2$, where $x_0$ represents milligrams of iron, $x_1$ represents milligrams of potassium, and $x_2$ represents milligrams of vitamin E.

## Step 2: List all the constraints
The constraints are as follows:
- $x_0 \geq 9$ (kidney support index for milligrams of iron)
- $11x_0 \leq 76$ (muscle growth index for milligrams of iron)
- $x_1 \geq 1$ (kidney support index for milligrams of potassium)
- $9x_1 \leq 76$ (muscle growth index for milligrams of potassium)
- $7x_2 \leq 86$ (kidney support index for milligrams of vitamin E)
- $11x_2 \leq 76$ (muscle growth index for milligrams of vitamin E)
- $9x_0 + x_1 + 7x_2 \geq 18$ (total combined kidney support index)
- $x_0^2 + x_2^2 \geq 11$ (total combined kidney support index from milligrams of iron and vitamin E)
- $x_1^2 + x_2^2 \geq 25$ (total combined kidney support index from milligrams of potassium and vitamin E)
- $x_0^2 + x_1^2 + x_2^2 \geq 18$ (total combined kidney support index from all)
- $11x_0 + 9x_1 + 11x_2 \geq 18$ (total combined muscle growth index)
- $x_0 + x_1 + x_2 \geq 18$ (total combined muscle growth index from all)
- $x_0^2 + x_1^2 \geq 16$ (total combined muscle growth index from milligrams of iron and potassium)
- $x_0^2 + x_2^2 \geq 23$ (total combined muscle growth index from milligrams of iron and vitamin E)
- $x_1^2 + x_2^2 \geq 10$ (total combined muscle growth index from milligrams of potassium and vitamin E)
- $-9x_1 + 7x_2 \geq 0$
- $2x_0^2 - 4x_1^2 \geq 0$
- $9x_0 + x_1 \leq 44$ (total combined kidney support index from milligrams of iron and potassium)
- $x_1^2 + x_2^2 \leq 66$ (total combined kidney support index from milligrams of potassium and vitamin E)
- $9x_1 + 11x_2 \leq 44$ (total combined muscle growth index from milligrams of potassium and vitamin E)
- $11x_0 + 11x_2 \leq 35$ (total combined muscle growth index from milligrams of iron and vitamin E)

## Step 3: Convert the problem into Gurobi code
```python
import gurobi

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

    # Define the variables
    x0 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="milligrams_of_iron")
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="milligrams_of_potassium")
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="milligrams_of_vitamin_E")

    # Objective function
    model.setObjective(6.91 * x0**2 + 9.46 * x0 * x1 + 8.04 * x2**2 + 1.53 * x1 + 2.22 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(x0 >= 9, name="kidney_support_index_iron")
    model.addConstr(11 * x0 <= 76, name="muscle_growth_index_iron")
    model.addConstr(x1 >= 1, name="kidney_support_index_potassium")
    model.addConstr(9 * x1 <= 76, name="muscle_growth_index_potassium")
    model.addConstr(7 * x2 <= 86, name="kidney_support_index_vitamin_E")
    model.addConstr(11 * x2 <= 76, name="muscle_growth_index_vitamin_E")

    model.addConstr(9 * x0 + x1 + 7 * x2 >= 18, name="total_kidney_support_index")
    model.addConstr(x0**2 + x2**2 >= 11, name="kidney_support_index_iron_vitamin_E")
    model.addConstr(x1**2 + x2**2 >= 25, name="kidney_support_index_potassium_vitamin_E")
    model.addConstr(x0**2 + x1**2 + x2**2 >= 18, name="total_kidney_support_index_all")

    model.addConstr(11 * x0 + 9 * x1 + 11 * x2 >= 18, name="total_muscle_growth_index")
    model.addConstr(x0 + x1 + x2 >= 18, name="total_muscle_growth_index_all")

    model.addConstr(x0**2 + x1**2 >= 16, name="muscle_growth_index_iron_potassium")
    model.addConstr(x0**2 + x2**2 >= 23, name="muscle_growth_index_iron_vitamin_E")
    model.addConstr(x1**2 + x2**2 >= 10, name="muscle_growth_index_potassium_vitamin_E")

    model.addConstr(-9 * x1 + 7 * x2 >= 0, name="constraint_1")
    model.addConstr(2 * x0**2 - 4 * x1**2 >= 0, name="constraint_2")

    model.addConstr(9 * x0 + x1 <= 44, name="kidney_support_index_iron_potassium")
    model.addConstr(x1**2 + x2**2 <= 66, name="kidney_support_index_potassium_vitamin_E_2")
    model.addConstr(9 * x1 + 11 * x2 <= 44, name="muscle_growth_index_potassium_vitamin_E")
    model.addConstr(11 * x0 + 11 * x2 <= 35, name="muscle_growth_index_iron_vitamin_E_2")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print("Milligrams of iron: ", x0.varValue)
        print("Milligrams of potassium: ", x1.varValue)
        print("Milligrams of vitamin E: ", x2.varValue)
        print("Objective function value: ", model.objVal)
    else:
        print("No optimal solution found.")

optimize()
```