## Step 1: Define the symbolic representation of the variables
The variables are defined as follows:
- $x_1$ represents milligrams of vitamin B5
- $x_2$ represents milligrams of zinc
- $x_3$ represents milligrams of vitamin B7
- $x_4$ represents milligrams of vitamin B4
- $x_5$ represents milligrams of calcium

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $5.81x_1 + 4.93x_2 + 5.73x_3 + 8.21x_4 + 8.07x_5$.

## 3: Define the constraints in symbolic notation
The constraints are:
- $5x_1 + 20x_2 + 31x_3 + 14x_4 + 31x_5 \leq 601$ (energy stability index upper bound)
- $5x_1 \geq 0$ and $x_1$ can be fractional
- $20x_2 \geq 0$ and $x_2$ can be fractional
- $31x_3 \geq 0$ and $x_3$ can be fractional
- $14x_4 \geq 0$ and $x_4$ can be fractional
- $31x_5 \geq 0$ and $x_5$ can be fractional
- $5x_1 + 20x_2 + 31x_3 \geq 69$
- $5x_1 + 20x_2 + 14x_4 \geq 69$
- $5x_1 + 20x_2 + 31x_3 \geq 80$
- $5x_1 + 20x_2 + 14x_4 \geq 80$
- $5x_1 + 31x_5 \leq 486$
- $20x_2 + 31x_3 \leq 213$
- $5x_1 + 20x_2 + 31x_3 + 14x_4 + 31x_5 \leq 213$

## 4: Create a symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'milligrams of vitamin B5'), 
        ('x2', 'milligrams of zinc'), 
        ('x3', 'milligrams of vitamin B7'), 
        ('x4', 'milligrams of vitamin B4'), 
        ('x5', 'milligrams of calcium')
    ], 
    'objective_function': '5.81*x1 + 4.93*x2 + 5.73*x3 + 8.21*x4 + 8.07*x5', 
    'constraints': [
        '5*x1 + 20*x2 + 31*x3 + 14*x4 + 31*x5 <= 601',
        '5*x1 + 20*x2 + 31*x3 >= 69',
        '5*x1 + 20*x2 + 14*x4 >= 69',
        '5*x1 + 20*x2 + 31*x3 >= 80',
        '5*x1 + 20*x2 + 14*x4 >= 80',
        '5*x1 + 31*x5 <= 486',
        '20*x2 + 31*x3 <= 213',
        '5*x1 + 20*x2 + 31*x3 + 14*x4 + 31*x5 <= 213'
    ]
}
```

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

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

    # Define variables
    x1 = model.addVar(name="x1", lb=0)  # milligrams of vitamin B5
    x2 = model.addVar(name="x2", lb=0)  # milligrams of zinc
    x3 = model.addVar(name="x3", lb=0)  # milligrams of vitamin B7
    x4 = model.addVar(name="x4", lb=0)  # milligrams of vitamin B4
    x5 = model.addVar(name="x5", lb=0)  # milligrams of calcium

    # Objective function
    model.setObjective(5.81*x1 + 4.93*x2 + 5.73*x3 + 8.21*x4 + 8.07*x5, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(5*x1 + 20*x2 + 31*x3 + 14*x4 + 31*x5 <= 601)
    model.addConstr(5*x1 + 20*x2 + 31*x3 >= 69)
    model.addConstr(5*x1 + 20*x2 + 14*x4 >= 69)
    model.addConstr(5*x1 + 20*x2 + 31*x3 >= 80)
    model.addConstr(5*x1 + 20*x2 + 14*x4 >= 80)
    model.addConstr(5*x1 + 31*x5 <= 486)
    model.addConstr(20*x2 + 31*x3 <= 213)
    model.addConstr(5*x1 + 20*x2 + 31*x3 + 14*x4 + 31*x5 <= 213)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of vitamin B5: {x1.varValue}")
        print(f"Milligrams of zinc: {x2.varValue}")
        print(f"Milligrams of vitamin B7: {x3.varValue}")
        print(f"Milligrams of vitamin B4: {x4.varValue}")
        print(f"Milligrams of calcium: {x5.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

optimize_problem()
```