## Step 1: Define the symbolic representation of the problem
The problem involves minimizing an objective function subject to several constraints. Let's define the symbolic variables:
- $x_0$ represents 'milligrams of vitamin D'
- $x_1$ represents 'milligrams of vitamin B12'
- $x_2$ represents 'milligrams of vitamin E'

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $5.42x_0 + 3.19x_1 + 1.61x_2$.

## 3: List the constraints in symbolic notation
The constraints given are:
- $7x_0 + 6x_1 + 8x_2 \geq 41$ (immune support index from $x_0$ and $x_1$)
- $7x_0 + 6x_1 \geq 22$ (immune support index from $x_0$ and $x_1$)
- $7x_0 + 6x_1 + 8x_2 \geq 22$ (total immune support index)
- $5x_0 + 6x_2 \geq 15$ (cardiovascular support index from $x_0$ and $x_2$)
- $5x_0 + 2x_1 + 6x_2 \geq 15$ (total cardiovascular support index)
- $8x_1 + 7x_2 \geq 35$ (kidney support index from $x_1$ and $x_2$)
- $1x_0 + 8x_1 + 7x_2 \geq 35$ (total kidney support index)
- $6x_0 + 3x_2 \geq 28$ (muscle growth index from $x_0$ and $x_2$)
- $7x_1 + 3x_2 \geq 16$ (muscle growth index from $x_1$ and $x_2$)
- $6x_0 + 7x_1 + 3x_2 \geq 16$ (total muscle growth index)
- $7x_0 + 6x_1 + 8x_2 \leq 110$ (total immune support index upper bound)
- $5x_0 + 2x_1 + 6x_2 \leq 48$ (cardiovascular support index from $x_0$, $x_1$, and $x_2$ upper bound, corrected to reflect $x_0$ and $x_2$)
- $5x_0 + 2x_1 + 6x_2 \leq 64$ (total cardiovascular support index upper bound)
- $1x_0 + 7x_2 \leq 114$ (kidney support index from $x_0$ and $x_2$ upper bound)
- $8x_1 + 7x_2 \leq 108$ (kidney support index from $x_1$ and $x_2$ upper bound)
- $6x_0 + 7x_1 + 3x_2 \leq 60$ (total muscle growth index upper bound)
- $x_0$ and $x_1$ can be fractional, but $x_2$ must be an integer.

## 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ('x0', 'milligrams of vitamin D'), 
        ('x1', 'milligrams of vitamin B12'), 
        ('x2', 'milligrams of vitamin E')
    ], 
    'objective_function': '5.42*x0 + 3.19*x1 + 1.61*x2', 
    'constraints': [
        '7*x0 + 6*x1 + 8*x2 >= 41',
        '7*x0 + 6*x1 >= 22',
        '7*x0 + 6*x1 + 8*x2 >= 22',
        '5*x0 + 6*x2 >= 15',
        '5*x0 + 2*x1 + 6*x2 >= 15',
        '8*x1 + 7*x2 >= 35',
        'x0 + 8*x1 + 7*x2 >= 35',
        '6*x0 + 3*x2 >= 28',
        '7*x1 + 3*x2 >= 16',
        '6*x0 + 7*x1 + 3*x2 >= 16',
        '7*x0 + 6*x1 + 8*x2 <= 110',
        '5*x0 + 2*x1 + 6*x2 <= 48',
        '5*x0 + 2*x1 + 6*x2 <= 64',
        'x0 + 7*x2 <= 114',
        '8*x1 + 7*x2 <= 108',
        '6*x0 + 7*x1 + 3*x2 <= 60'
    ]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi

def optimize_vitamins():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name="x0", lb=0, ub=None)  # milligrams of vitamin D
    x1 = model.addVar(name="x1", lb=0, ub=None)  # milligrams of vitamin B12
    x2 = model.addVar(name="x2", lb=0, ub=None, vtype=gurobi.GRB.INTEGER)  # milligrams of vitamin E

    # Objective function
    model.setObjective(5.42 * x0 + 3.19 * x1 + 1.61 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(7 * x0 + 6 * x1 + 8 * x2 >= 41)  
    model.addConstr(7 * x0 + 6 * x1 >= 22)
    model.addConstr(7 * x0 + 6 * x1 + 8 * x2 >= 22)
    model.addConstr(5 * x0 + 6 * x2 >= 15)
    model.addConstr(5 * x0 + 2 * x1 + 6 * x2 >= 15)
    model.addConstr(8 * x1 + 7 * x2 >= 35)
    model.addConstr(x0 + 8 * x1 + 7 * x2 >= 35)
    model.addConstr(6 * x0 + 3 * x2 >= 28)
    model.addConstr(7 * x1 + 3 * x2 >= 16)
    model.addConstr(6 * x0 + 7 * x1 + 3 * x2 >= 16)
    model.addConstr(7 * x0 + 6 * x1 + 8 * x2 <= 110)
    model.addConstr(5 * x0 + 2 * x1 + 6 * x2 <= 48)
    model.addConstr(5 * x0 + 2 * x1 + 6 * x2 <= 64)
    model.addConstr(x0 + 7 * x2 <= 114)
    model.addConstr(8 * x1 + 7 * x2 <= 108)
    model.addConstr(6 * x0 + 7 * x1 + 3 * x2 <= 60)

    # Solve the model
    model.optimize()

    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of vitamin D: {x0.varValue}")
        print(f"Milligrams of vitamin B12: {x1.varValue}")
        print(f"Milligrams of vitamin E: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

optimize_vitamins()
```