## Step 1: Define the symbolic representation of the variables
The variables are ['milligrams of iron', 'milligrams of potassium', 'milligrams of vitamin E']. Let's denote them as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the natural language objects into symbolic notation
The symbolic representation of the variables is:
- $x_0$ = milligrams of iron
- $x_1$ = milligrams of potassium
- $x_2$ = milligrams of vitamin E

## 3: Define the objective function in symbolic notation
The objective function to minimize is $6.91x_0^2 + 9.46x_0x_1 + 8.04x_2^2 + 1.53x_1 + 2.22x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
- $9x_0 \leq 86$ (kidney support index for $x_0$)
- $11x_0 \leq 76$ (muscle growth index for $x_0$)
- $1x_1 \leq 86$ (kidney support index for $x_1$)
- $9x_1 \leq 76$ (muscle growth index for $x_1$)
- $7x_2 \leq 86$ (kidney support index for $x_2$)
- $11x_2 \leq 76$ (muscle growth index for $x_2$)
- $9x_0^2 + 7x_2^2 \geq 11$ (combined kidney support index)
- $1x_1^2 + 7x_2^2 \geq 25$ (combined kidney support index)
- $9x_0^2 + 1x_1^2 + 7x_2^2 \geq 18$ (combined kidney support index)
- $9x_0 + 1x_1 + 7x_2 \geq 18$ (combined kidney support index)
- $11x_0^2 + 9x_1^2 \geq 16$ (combined muscle growth index)
- $11x_0^2 + 11x_2^2 \geq 23$ (combined muscle growth index)
- $9x_1^2 + 11x_2^2 \geq 10$ (combined muscle growth index)
- $11x_0 + 9x_1 + 11x_2 \geq 18$ (combined muscle growth index)
- $11x_0 + 9x_1 + 11x_2 \geq 18$ (combined muscle growth index, duplicate)
- $-9x_1 + 7x_2 \geq 0$
- $2x_0^2 - 4x_1^2 \geq 0$
- $9x_0 + 1x_1 \leq 44$
- $1x_1^2 + 7x_2^2 \leq 66$
- $9x_1 + 11x_2 \leq 44$
- $11x_0 + 11x_2 \leq 35$

## 5: Create the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'milligrams of iron'), 
        ('x1', 'milligrams of potassium'), 
        ('x2', 'milligrams of vitamin E')
    ], 
    'objective_function': '6.91*x0^2 + 9.46*x0*x1 + 8.04*x2^2 + 1.53*x1 + 2.22*x2', 
    'constraints': [
        '9*x0 <= 86', 
        '11*x0 <= 76', 
        '1*x1 <= 86', 
        '9*x1 <= 76', 
        '7*x2 <= 86', 
        '11*x2 <= 76', 
        '9*x0^2 + 7*x2^2 >= 11', 
        '1*x1^2 + 7*x2^2 >= 25', 
        '9*x0^2 + 1*x1^2 + 7*x2^2 >= 18', 
        '9*x0 + 1*x1 + 7*x2 >= 18', 
        '11*x0^2 + 9*x1^2 >= 16', 
        '11*x0^2 + 11*x2^2 >= 23', 
        '9*x1^2 + 11*x2^2 >= 10', 
        '11*x0 + 9*x1 + 11*x2 >= 18', 
        '-9*x1 + 7*x2 >= 0', 
        '2*x0^2 - 4*x1^2 >= 0', 
        '9*x0 + 1*x1 <= 44', 
        '1*x1^2 + 7*x2^2 <= 66', 
        '9*x1 + 11*x2 <= 44', 
        '11*x0 + 11*x2 <= 35'
    ]
}
```

## 6: Write the Gurobi code
```python
import gurobi

def solve_optimization_problem():
    # Create a new 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")

    # Define the 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)

    # Add constraints
    model.addConstr(9 * x0 <= 86)
    model.addConstr(11 * x0 <= 76)
    model.addConstr(x1 <= 86)
    model.addConstr(9 * x1 <= 76)
    model.addConstr(7 * x2 <= 86)
    model.addConstr(11 * x2 <= 76)
    model.addConstr(9 * x0**2 + 7 * x2**2 >= 11)
    model.addConstr(x1**2 + 7 * x2**2 >= 25)
    model.addConstr(9 * x0**2 + x1**2 + 7 * x2**2 >= 18)
    model.addConstr(9 * x0 + x1 + 7 * x2 >= 18)
    model.addConstr(11 * x0**2 + 9 * x1**2 >= 16)
    model.addConstr(11 * x0**2 + 11 * x2**2 >= 23)
    model.addConstr(9 * x1**2 + 11 * x2**2 >= 10)
    model.addConstr(11 * x0 + 9 * x1 + 11 * x2 >= 18)
    model.addConstr(-9 * x1 + 7 * x2 >= 0)
    model.addConstr(2 * x0**2 - 4 * x1**2 >= 0)
    model.addConstr(9 * x0 + x1 <= 44)
    model.addConstr(x1**2 + 7 * x2**2 <= 66)
    model.addConstr(9 * x1 + 11 * x2 <= 44)
    model.addConstr(11 * x0 + 11 * x2 <= 35)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.Status.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.")

solve_optimization_problem()
```