## Step 1: Define the symbolic representation of the problem
The problem involves three variables: 'milligrams of vitamin B12', 'milligrams of iron', and 'milligrams of zinc'. Let's denote these as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $4.94x_1 + 9.67x_2 + 2.41x_3$.

## 3: List the constraints in symbolic notation
1. $5.39x_1 + 3.4x_2 + 7.24x_3 \geq 9$ (cognitive performance index from all)
2. $5.39x_1 + 3.4x_2 \geq 13$ (cognitive performance index from $x_1$ and $x_2$)
3. $5.39x_1 + 3.4x_2 + 7.24x_3 \geq 13$ (cognitive performance index from all, redundant with 1 and 2)
4. $8.08x_1 + 5.23x_2 \geq 29$ (immune support index from $x_1$ and $x_2$)
5. $8.08x_1 + 5.23x_2 + 8.59x_3 \geq 29$ (immune support index from all)
6. $10.29x_1 + 13.7x_3 \geq 20$ (muscle growth index from $x_1$ and $x_3$)
7. $10.29x_1 + 5.27x_2 \geq 49$ (muscle growth index from $x_1$ and $x_2$)
8. $10.29x_1 + 5.27x_2 + 13.7x_3 \geq 49$ (muscle growth index from all)
9. $6x_1 - 5x_2 \geq 0$
10. $-3x_1 + 3x_3 \geq 0$
11. $5.39x_1 + 3.4x_2 \leq 34$ (cognitive performance index from $x_1$ and $x_2$)
12. $3.4x_2 + 7.24x_3 \leq 65$ (cognitive performance index from $x_2$ and $x_3$)
13. $8.08x_1 + 5.23x_2 \leq 194$ (immune support index from $x_1$ and $x_2$)
14. $8.08x_1 + 5.23x_2 + 8.59x_3 \leq 194$ (immune support index from all)
15. $10.29x_1 + 5.27x_2 + 13.7x_3 \leq 116$ (muscle growth index from all)

## 4: Define variable types
- $x_1$ (milligrams of vitamin B12) must be a whole number.
- $x_2$ (milligrams of iron) can be a fractional number.
- $x_3$ (milligrams of zinc) must be a non-fractional number.

## 5: Symbolic Representation
```json
{
    'sym_variables': [
        ('x1', 'milligrams of vitamin B12'),
        ('x2', 'milligrams of iron'),
        ('x3', 'milligrams of zinc')
    ],
    'objective_function': '4.94*x1 + 9.67*x2 + 2.41*x3',
    'constraints': [
        '5.39*x1 + 3.4*x2 + 7.24*x3 >= 9',
        '5.39*x1 + 3.4*x2 >= 13',
        '8.08*x1 + 5.23*x2 >= 29',
        '8.08*x1 + 5.23*x2 + 8.59*x3 >= 29',
        '10.29*x1 + 13.7*x3 >= 20',
        '10.29*x1 + 5.27*x2 >= 49',
        '10.29*x1 + 5.27*x2 + 13.7*x3 >= 49',
        '6*x1 - 5*x2 >= 0',
        '-3*x1 + 3*x3 >= 0',
        '5.39*x1 + 3.4*x2 <= 34',
        '3.4*x2 + 7.24*x3 <= 65',
        '8.08*x1 + 5.23*x2 <= 194',
        '8.08*x1 + 5.23*x2 + 8.59*x3 <= 194',
        '10.29*x1 + 5.27*x2 + 13.7*x3 <= 116'
    ]
}
```

## 6: Gurobi Code
```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="x1", vtype=gurobi.GRB.INTEGER)  # milligrams of vitamin B12
    x2 = model.addVar(name="x2")  # milligrams of iron
    x3 = model.addVar(name="x3", vtype=gurobi.GRB.INTEGER)  # milligrams of zinc

    # Objective function
    model.setObjective(4.94 * x1 + 9.67 * x2 + 2.41 * x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(5.39 * x1 + 3.4 * x2 + 7.24 * x3 >= 9)
    model.addConstr(5.39 * x1 + 3.4 * x2 >= 13)
    model.addConstr(8.08 * x1 + 5.23 * x2 >= 29)
    model.addConstr(8.08 * x1 + 5.23 * x2 + 8.59 * x3 >= 29)
    model.addConstr(10.29 * x1 + 13.7 * x3 >= 20)
    model.addConstr(10.29 * x1 + 5.27 * x2 >= 49)
    model.addConstr(10.29 * x1 + 5.27 * x2 + 13.7 * x3 >= 49)
    model.addConstr(6 * x1 - 5 * x2 >= 0)
    model.addConstr(-3 * x1 + 3 * x3 >= 0)
    model.addConstr(5.39 * x1 + 3.4 * x2 <= 34)
    model.addConstr(3.4 * x2 + 7.24 * x3 <= 65)
    model.addConstr(8.08 * x1 + 5.23 * x2 <= 194)
    model.addConstr(8.08 * x1 + 5.23 * x2 + 8.59 * x3 <= 194)
    model.addConstr(10.29 * x1 + 5.27 * x2 + 13.7 * x3 <= 116)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"x1 (milligrams of vitamin B12): {x1.varValue}")
        print(f"x2 (milligrams of iron): {x2.varValue}")
        print(f"x3 (milligrams of zinc): {x3.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```