## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'milligrams of vitamin B3' and 'milligrams of potassium'. Let's denote 'milligrams of vitamin B3' as $x_1$ and 'milligrams of potassium' as $x_2$. The objective function to maximize is $1.47x_1 + 4.67x_2$.

## Step 2: Translate the constraints into symbolic notation
The constraints given are:
1. The muscle growth index of milligrams of vitamin B3 is 2: $2x_1$.
2. Milligrams of vitamin B3 have a cardiovascular support index of 16: $16x_1$.
3. Milligrams of potassium each have a muscle growth index of 3: $3x_2$.
4. Milligrams of potassium each have a cardiovascular support index of 21: $21x_2$.
5. The total combined muscle growth index from milligrams of vitamin B3 and milligrams of potassium should be 16 or more: $2x_1 + 3x_2 \geq 16$.
6. The total combined cardiovascular support index from milligrams of vitamin B3 and milligrams of potassium should be equal to or greater than 24: $16x_1 + 21x_2 \geq 24$.
7. Minus ten times the number of milligrams of vitamin B3, plus 3 times the number of milligrams of potassium has to be at least zero: $-10x_1 + 3x_2 \geq 0$.
8. The total combined muscle growth index from milligrams of vitamin B3 plus milligrams of potassium should be at most 57: $2x_1 + 3x_2 \leq 57$.
9. The total combined cardiovascular support index from milligrams of vitamin B3 and milligrams of potassium must be 64 or less: $16x_1 + 21x_2 \leq 64$.

## 3: Define the symbolic representation
The symbolic representation of the problem is:
- Variables: $x_1$ for 'milligrams of vitamin B3', $x_2$ for 'milligrams of potassium'.
- Objective function: Maximize $1.47x_1 + 4.67x_2$.
- Constraints:
  1. $2x_1 + 3x_2 \geq 16$
  2. $16x_1 + 21x_2 \geq 24$
  3. $-10x_1 + 3x_2 \geq 0$
  4. $2x_1 + 3x_2 \leq 57$
  5. $16x_1 + 21x_2 \leq 64$

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

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

# Define the variables
x1 = model.addVar(name="milligrams_of_vitamin_B3", lb=0)  # No lower bound specified, assuming 0
x2 = model.addVar(name="milligrams_of_potassium", lb=0)  # No lower bound specified, assuming 0

# Define the objective function
model.setObjective(1.47 * x1 + 4.67 * x2, gurobi.GRB.MAXIMIZE)

# Add constraints
model.addConstr(2 * x1 + 3 * x2 >= 16, name="muscle_growth_index_min")
model.addConstr(16 * x1 + 21 * x2 >= 24, name="cardiovascular_support_index_min")
model.addConstr(-10 * x1 + 3 * x2 >= 0, name="vitamin_potassium_balance")
model.addConstr(2 * x1 + 3 * x2 <= 57, name="muscle_growth_index_max")
model.addConstr(16 * x1 + 21 * x2 <= 64, name="cardiovascular_support_index_max")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Milligrams of vitamin B3: {x1.varValue}")
    print(f"Milligrams of potassium: {x2.varValue}")
    print(f"Objective function value: {model.objVal}")
else:
    print("No optimal solution found.")
```

## 5: Provide the symbolic representation in the required format
```json
{
    'sym_variables': [('x1', 'milligrams of vitamin B3'), ('x2', 'milligrams of potassium')],
    'objective_function': '1.47*x1 + 4.67*x2',
    'constraints': [
        '2*x1 + 3*x2 >= 16',
        '16*x1 + 21*x2 >= 24',
        '-10*x1 + 3*x2 >= 0',
        '2*x1 + 3*x2 <= 57',
        '16*x1 + 21*x2 <= 64'
    ]
}
```