## Step 1: Define the symbolic representation of the variables
The variables are 'milligrams of vitamin E', 'milligrams of vitamin B12', and 'milligrams of vitamin A', 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 $8x_1 + 2x_2 + x_3$.

## Step 3: Convert the constraints into a symbolic representation
The constraints are:
1. $31x_1$ (no constraint directly on $x_1$, but a coefficient for muscle growth index),
2. $14x_2$,
3. $28x_3$,
4. $31x_1 + 28x_3 \geq 26$,
5. $14x_2 + 28x_3 \geq 41$,
6. $31x_1 + 14x_2 + 28x_3 \geq 41$,
7. $4x_1 - 3x_3 \geq 0$,
8. $8x_2 - 2x_3 \geq 0$.

## 4: Define the symbolic representation of the problem
The symbolic representation is:
- Variables: $(x_1, 'milligrams of vitamin E'), (x_2, 'milligrams of vitamin B12'), (x_3, 'milligrams of vitamin A')$
- Objective function: $8x_1 + 2x_2 + x_3$
- Constraints:
  1. $31x_1 + 28x_3 \geq 26$
  2. $14x_2 + 28x_3 \geq 41$
  3. $31x_1 + 14x_2 + 28x_3 \geq 41$
  4. $4x_1 - 3x_3 \geq 0$
  5. $8x_2 - 2x_3 \geq 0$

## 5: Implement the problem in Gurobi
To solve this problem using Gurobi, we will use Python.

```python
import gurobi

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

# Define the variables
x1 = model.addVar(name="milligrams_of_vitamin_E", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x2 = model.addVar(name="milligrams_of_vitamin_B12", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x3 = model.addVar(name="milligrams_of_vitamin_A", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)

# Set the objective function
model.setObjective(8*x1 + 2*x2 + x3, gurobi.GRB.MINIMIZE)

# Add constraints
model.addConstr(31*x1 + 28*x3 >= 26, name="constraint_1")
model.addConstr(14*x2 + 28*x3 >= 41, name="constraint_2")
model.addConstr(31*x1 + 14*x2 + 28*x3 >= 41, name="constraint_3")
model.addConstr(4*x1 - 3*x3 >= 0, name="constraint_4")
model.addConstr(8*x2 - 2*x3 >= 0, name="constraint_5")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objVal)
    print("Milligrams of vitamin E: ", x1.varValue)
    print("Milligrams of vitamin B12: ", x2.varValue)
    print("Milligrams of vitamin A: ", x3.varValue)
else:
    print("The model is infeasible")
```

## 6: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [('x1', 'milligrams of vitamin E'), ('x2', 'milligrams of vitamin B12'), ('x3', 'milligrams of vitamin A')],
    'objective_function': '8*x1 + 2*x2 + x3',
    'constraints': [
        '31*x1 + 28*x3 >= 26',
        '14*x2 + 28*x3 >= 41',
        '31*x1 + 14*x2 + 28*x3 >= 41',
        '4*x1 - 3*x3 >= 0',
        '8*x2 - 2*x3 >= 0'
    ]
}
```