## Step 1: Define the symbolic representation of the variables
The variables are 'milligrams of magnesium' and 'grams of carbohydrates', which we will denote as $x_1$ and $x_2$ respectively.

## Step 2: Translate the given attributes into symbolic notation
Given attributes are:
- $r_0$: immune support index, with $x_0 = 8$, $x_1 = 2$
- $r_1$: cognitive performance index, with $x_0 = 20$, $x_1 = 5$
- $r_2$: muscle growth index, with $x_0 = 1$, $x_1 = 7$
- $r_3$: energy stability index, with $x_0 = 16$, $x_1 = 18$

However, it seems there was an initial confusion in interpreting $x_0$ and $x_1$. Based on the problem statement, we understand that:
- The immune support index of milligrams of magnesium ($x_1$) is 8.
- The cognitive performance index of milligrams of magnesium ($x_1$) is 20.
- The muscle growth index of milligrams of magnesium ($x_1$) is 1.
- The energy stability index of milligrams of magnesium ($x_1$) is 16.
- The immune support index of grams of carbohydrates ($x_2$) is 2.
- The cognitive performance index of grams of carbohydrates ($x_2$) is 5.
- The muscle growth index of grams of carbohydrates ($x_2$) is 7.
- The energy stability index of grams of carbohydrates ($x_2$) is 18.

## 3: Formulate the objective function
The objective function to maximize is $7.49x_1^2 + 1.91x_2^2 + 1.27x_2$.

## 4: List all constraints
1. $8x_1 \leq 72$
2. $20x_1 \leq 136$
3. $1x_1 \leq 50$
4. $16x_1 \leq 119$
5. $2x_2 \leq 72$
6. $5x_2 \leq 136$
7. $7x_2 \leq 50$
8. $18x_2 \leq 119$
9. $8^2x_1^2 + 2^2x_2^2 \geq 26$
10. $20x_1 + 5x_2 \geq 38$
11. $1x_1 + 7x_2 \geq 9$
12. $16x_1 + 18x_2 \geq 32$
13. $-10x_1 + 9x_2 \geq 0$
14. $8x_1 + 2x_2 \leq 69$
15. $20x_1^2 + 5^2x_2^2 \leq 122$
16. $20x_1 + 5x_2 \leq 122$
17. $1x_1 + 7x_2 \leq 44$
18. $16x_1^2 + 18^2x_2^2 \leq 59$
19. $16x_1 + 18x_2 \leq 59$
20. $x_1$ is an integer.

## 5: Symbolic Representation
```json
{
'sym_variables': [('x1', 'milligrams of magnesium'), ('x2', 'grams of carbohydrates')],
'objective_function': '7.49*x1^2 + 1.91*x2^2 + 1.27*x2',
'constraints': [
    '8*x1 <= 72',
    '20*x1 <= 136',
    '1*x1 <= 50',
    '16*x1 <= 119',
    '2*x2 <= 72',
    '5*x2 <= 136',
    '7*x2 <= 50',
    '18*x2 <= 119',
    '8^2*x1^2 + 2^2*x2^2 >= 26',
    '20*x1 + 5*x2 >= 38',
    '1*x1 + 7*x2 >= 9',
    '16*x1 + 18*x2 >= 32',
    '-10*x1 + 9*x2 >= 0',
    '8*x1 + 2*x2 <= 69',
    '20*x1^2 + 5^2*x2^2 <= 122',
    '20*x1 + 5*x2 <= 122',
    '1*x1 + 7*x2 <= 44',
    '16*x1^2 + 18^2*x2^2 <= 59',
    '16*x1 + 18*x2 <= 59',
    'x1 >= 0' # Assuming x1 and x2 are non-negative
    ]
}
```

## 6: Gurobi Code
```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="milligrams_of_magnesium", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="grams_of_carbohydrates")

    # Objective function
    model.setObjective(7.49 * x1**2 + 1.91 * x2**2 + 1.27 * x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(8 * x1 <= 72)
    model.addConstr(20 * x1 <= 136)
    model.addConstr(x1 <= 50)
    model.addConstr(16 * x1 <= 119)

    model.addConstr(2 * x2 <= 72)
    model.addConstr(5 * x2 <= 136)
    model.addConstr(7 * x2 <= 50)
    model.addConstr(18 * x2 <= 119)

    model.addConstr(8**2 * x1**2 + 2**2 * x2**2 >= 26)
    model.addConstr(20 * x1 + 5 * x2 >= 38)
    model.addConstr(x1 + 7 * x2 >= 9)
    model.addConstr(16 * x1 + 18 * x2 >= 32)
    model.addConstr(-10 * x1 + 9 * x2 >= 0)

    model.addConstr(8 * x1 + 2 * x2 <= 69)
    model.addConstr(20 * x1**2 + 5**2 * x2**2 <= 122)
    model.addConstr(20 * x1 + 5 * x2 <= 122)
    model.addConstr(x1 + 7 * x2 <= 44)
    model.addConstr(16 * x1**2 + 18**2 * x2**2 <= 59)
    model.addConstr(16 * x1 + 18 * x2 <= 59)

    # Solve the model
    model.optimize()

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

solve_optimization_problem()
```