## Step 1: Define the symbolic representation of the variables
The variables are 'grams of carbohydrates', 'milligrams of vitamin B12', and 'milligrams of vitamin D', which can be represented symbolically as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $4 \times (\text{grams of carbohydrates}) + 6 \times (\text{milligrams of vitamin B12}) + 3 \times (\text{milligrams of vitamin D})$. In symbolic terms, this is $4x_1 + 6x_2 + 3x_3$.

## 3: List the constraints in symbolic notation
1. $18x_1 = 18$ (muscle growth index of grams of carbohydrates)
2. $13x_1 = 13$ (energy stability index of grams of carbohydrates)
3. $5x_1 = 5$ (immune support index of grams of carbohydrates)
4. $21x_1 = 21$ (cognitive performance index of grams of carbohydrates)
5. $21x_2 = 21$ (muscle growth index of milligrams of vitamin B12)
6. $9x_2 = 9$ (energy stability index of milligrams of vitamin B12)
7. $15x_2 = 15$ (immune support index of milligrams of vitamin B12)
8. $5x_2 = 5$ (cognitive performance index of milligrams of vitamin B12)
9. $2x_3 = 2$ (muscle growth index of milligrams of vitamin D)
10. $23x_3 = 23$ (energy stability index of milligrams of vitamin D)
11. $10x_3 = 10$ (immune support index of milligrams of vitamin D)
12. $8x_3 = 8$ (cognitive performance index of milligrams of vitamin D)
13. $21x_2 + 2x_3 \geq 47$ (total muscle growth index from $x_2$ and $x_3$)
14. $18x_1 + 2x_3 \geq 48$ (total muscle growth index from $x_1$ and $x_3$)
15. $18x_1 + 21x_2 + 2x_3 \geq 48$ (total muscle growth index from $x_1$, $x_2$, and $x_3$)
16. $13x_1 + 23x_3 \geq 39$ (total energy stability index from $x_1$ and $x_3$)
17. $9x_2 + 23x_3 \geq 58$ (total energy stability index from $x_2$ and $x_3$)
18. $13x_1 + 9x_2 + 23x_3 \geq 58$ (total energy stability index from $x_1$, $x_2$, and $x_3$)
19. $5x_1 + 10x_3 \geq 22$ (total immune support index from $x_1$ and $x_3$)
20. $5x_1 + 15x_2 \geq 32$ (total immune support index from $x_1$ and $x_2$)
21. $5x_1 + 15x_2 + 10x_3 \geq 31$ (total immune support index from $x_1$, $x_2$, and $x_3$)
22. $5x_1 + 15x_2 + 10x_3 \geq 31$ (same as above, redundant)
23. $21x_1 + 8x_3 \geq 31$ (total cognitive performance index from $x_1$ and $x_3$)
24. $21x_1 + 5x_2 + 8x_3 \geq 31$ (total cognitive performance index from $x_1$, $x_2$, and $x_3$)
25. $-3x_1 + 7x_3 \geq 0$ (linear constraint)
26. $10x_1 - 8x_2 \geq 0$ (linear constraint)
27. $5x_1 + 15x_2 + 10x_3 \leq 56$ (upper bound on total immune support index)
28. $21x_1 + 5x_2 + 8x_3 \leq 111$ (upper bound on total cognitive performance index)

## 4: Create the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'grams of carbohydrates'),
        ('x2', 'milligrams of vitamin B12'),
        ('x3', 'milligrams of vitamin D')
    ],
    'objective_function': '4*x1 + 6*x2 + 3*x3',
    'constraints': [
        '18*x1 = 18',
        '13*x1 = 13',
        '5*x1 = 5',
        '21*x1 = 21',
        '21*x2 = 21',
        '9*x2 = 9',
        '15*x2 = 15',
        '5*x2 = 5',
        '2*x3 = 2',
        '23*x3 = 23',
        '10*x3 = 10',
        '8*x3 = 8',
        '21*x2 + 2*x3 >= 47',
        '18*x1 + 2*x3 >= 48',
        '18*x1 + 21*x2 + 2*x3 >= 48',
        '13*x1 + 23*x3 >= 39',
        '9*x2 + 23*x3 >= 58',
        '13*x1 + 9*x2 + 23*x3 >= 58',
        '5*x1 + 10*x3 >= 22',
        '5*x1 + 15*x2 >= 32',
        '5*x1 + 15*x2 + 10*x3 >= 31',
        '21*x1 + 8*x3 >= 31',
        '21*x1 + 5*x2 + 8*x3 >= 31',
        '-3*x1 + 7*x3 >= 0',
        '10*x1 - 8*x2 >= 0',
        '5*x1 + 15*x2 + 10*x3 <= 56',
        '21*x1 + 5*x2 + 8*x3 <= 111'
    ]
}
```

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

# Create a new Gurobi model
m = gurobi.Model()

# Define the variables
x1 = m.addVar(name="x1", lb=0)  # grams of carbohydrates
x2 = m.addVar(name="x2", lb=0)  # milligrams of vitamin B12
x3 = m.addVar(name="x3", lb=0)  # milligrams of vitamin D

# Objective function
m.setObjective(4 * x1 + 6 * x2 + 3 * x3, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(18 * x1 == 18)
m.addConstr(13 * x1 == 13)
m.addConstr(5 * x1 == 5)
m.addConstr(21 * x1 == 21)
m.addConstr(21 * x2 == 21)
m.addConstr(9 * x2 == 9)
m.addConstr(15 * x2 == 15)
m.addConstr(5 * x2 == 5)
m.addConstr(2 * x3 == 2)
m.addConstr(23 * x3 == 23)
m.addConstr(10 * x3 == 10)
m.addConstr(8 * x3 == 8)
m.addConstr(21 * x2 + 2 * x3 >= 47)
m.addConstr(18 * x1 + 2 * x3 >= 48)
m.addConstr(18 * x1 + 21 * x2 + 2 * x3 >= 48)
m.addConstr(13 * x1 + 23 * x3 >= 39)
m.addConstr(9 * x2 + 23 * x3 >= 58)
m.addConstr(13 * x1 + 9 * x2 + 23 * x3 >= 58)
m.addConstr(5 * x1 + 10 * x3 >= 22)
m.addConstr(5 * x1 + 15 * x2 >= 32)
m.addConstr(5 * x1 + 15 * x2 + 10 * x3 >= 31)
m.addConstr(21 * x1 + 8 * x3 >= 31)
m.addConstr(21 * x1 + 5 * x2 + 8 * x3 >= 31)
m.addConstr(-3 * x1 + 7 * x3 >= 0)
m.addConstr(10 * x1 - 8 * x2 >= 0)
m.addConstr(5 * x1 + 15 * x2 + 10 * x3 <= 56)
m.addConstr(21 * x1 + 5 * x2 + 8 * x3 <= 111)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objval)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
    print("x3: ", x3.varValue)
else:
    print("The model is infeasible")
```