To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints in terms of these variables.

Let's denote:
- $x_1$ as the quantity of milligrams of magnesium,
- $x_2$ as the quantity of milligrams of vitamin B3.

The objective function to maximize is given by:
\[5.17x_1^2 + 2.62x_1x_2 + 5.21x_2^2 + 6.16x_1 + 4.47x_2\]

The constraints are as follows:
1. The muscle growth index of milligrams of magnesium is 17: $17x_1$
2. The energy stability index for milligrams of magnesium is 23: $23x_1$
3. Milligrams of vitamin B3 each have a muscle growth index of 10: $10x_2$
4. Milligrams of vitamin B3 each have an energy stability index of 5: $5x_2$
5. The total combined muscle growth index from milligrams of magnesium plus milligrams of vitamin B3 must be at least 102: $17x_1 + 10x_2 \geq 102$
6. The total combined energy stability index from milligrams of magnesium and milligrams of vitamin B3 has to be at least 27: $23x_1 + 5x_2 \geq 27$
7. $4x_1 - 2x_2 \geq 0$
8. The total combined muscle growth index from milligrams of magnesium, and milligrams of vitamin B3 must be equal to or less than 177: $17x_1 + 10x_2 \leq 177$
9. The total combined energy stability index from milligrams of magnesium plus milligrams of vitamin B3 has to be no more than 136: $23x_1 + 5x_2 \leq 136$

Given these definitions, the symbolic representation of the problem is:
```json
{
  'sym_variables': [('x1', 'milligrams of magnesium'), ('x2', 'milligrams of vitamin B3')],
  'objective_function': '5.17*x1**2 + 2.62*x1*x2 + 5.21*x2**2 + 6.16*x1 + 4.47*x2',
  'constraints': [
    '17*x1 + 10*x2 >= 102',
    '23*x1 + 5*x2 >= 27',
    '4*x1 - 2*x2 >= 0',
    '17*x1 + 10*x2 <= 177',
    '23*x1 + 5*x2 <= 136'
  ]
}
```

To implement this problem in Gurobi, we use the following Python code:
```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define variables
x1 = m.addVar(lb=0, name="milligrams_of_magnesium")
x2 = m.addVar(lb=0, name="milligrams_of_vitamin_B3")

# Set the objective function
m.setObjective(5.17*x1**2 + 2.62*x1*x2 + 5.21*x2**2 + 6.16*x1 + 4.47*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(17*x1 + 10*x2 >= 102, name="muscle_growth_index_min")
m.addConstr(23*x1 + 5*x2 >= 27, name="energy_stability_index_min")
m.addConstr(4*x1 - 2*x2 >= 0, name="additional_constraint")
m.addConstr(17*x1 + 10*x2 <= 177, name="muscle_growth_index_max")
m.addConstr(23*x1 + 5*x2 <= 136, name="energy_stability_index_max")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Milligrams of magnesium: {x1.x}")
    print(f"Milligrams of vitamin B3: {x2.x}")
else:
    print("No optimal solution found")
```