## Step 1: Define the symbolic representation of the variables
The variables are 'milligrams of vitamin B3' and 'milligrams of calcium', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Convert the given attributes into a usable format
The given attributes are:
- $r_0$: muscle growth index, with $x_0 = 3$ for 'milligrams of vitamin B3' and $x_0 = 3$ for 'milligrams of calcium', and an upper bound of 77.
- $r_1$: cardiovascular support index, with $x_0 = 1$ for 'milligrams of vitamin B3' and $x_0 = 4$ for 'milligrams of calcium', and an upper bound of 127.
- $r_2$: digestive support index, with $x_0 = 8$ for 'milligrams of vitamin B3' and $x_0 = 11$ for 'milligrams of calcium', and an upper bound of 162.

## 3: Express the objective function in terms of symbolic variables
The objective function to maximize is: $1 \cdot x_1 \cdot x_2 + 9 \cdot x_2^2 + 4 \cdot x_1 + 3 \cdot x_2$.

## 4: List all constraints in terms of symbolic variables
The constraints are:
1. $3x_1 = 3$ (muscle growth index of $x_1$)
2. $1x_1 = 1$ (cardiovascular support index of $x_1$)
3. $8x_1 = 8$ (digestive support index of $x_1$)
4. $3x_2 = 3$ (muscle growth index of $x_2$)
5. $4x_2 = 4$ (cardiovascular support index of $x_2$)
6. $11x_2 = 11$ (digestive support index of $x_2$)
7. $3x_1 + 3x_2 \geq 20$ (total muscle growth index)
8. $1^2x_1^2 + 4^2x_2^2 \geq 56$ (total cardiovascular support index)
9. $8x_1 + 11x_2 \geq 61$ (total digestive support index)
10. $6x_1^2 - 8x_2^2 \geq 0$
11. $3x_1 + 3x_2 \leq 66$ (total muscle growth index upper bound)
12. $1x_1^2 + 4x_2^2 \leq 74$ (total cardiovascular support index upper bound)
13. $8x_1 + 11x_2 \leq 95$ (total digestive support index upper bound)
14. $x_1$ is an integer (milligrams of vitamin B3 cannot be a fraction)
15. $x_2$ can be a real number (fractional amount of milligrams of calcium allowed)

## 5: Realize that some constraints are redundant or directly assign values
Constraints 1, 2, 3, 4, 5, and 6 directly assign values to $x_1$ and $x_2$ or are redundant given the others:
- From constraint 1, $x_1 = 1$.
- From constraint 2, this is consistent with $x_1 = 1$.
- From constraint 3, this is consistent with $x_1 = 1$.
- From constraint 4, $x_2 = 1$.
- From constraint 5, this is consistent with $x_2 = 1$.
- From constraint 6, this is consistent with $x_2 = 1$.

## 6: Apply the directly assigned values to simplify the problem
Given $x_1 = 1$ and $x_2 = 1$, let's check if these values satisfy all constraints and calculate the objective function.

## 7: Check if the assigned values satisfy all constraints
1. $3 \cdot 1 = 3$
2. $1 \cdot 1 = 1$
3. $8 \cdot 1 = 8$
4. $3 \cdot 1 = 3$
5. $4 \cdot 1 = 4$
6. $11 \cdot 1 = 11$
7. $3 \cdot 1 + 3 \cdot 1 = 6 \geq 20$ is false.
Given that constraint 7 is not satisfied, $x_1 = 1$ and $x_2 = 1$ is not a feasible solution.

## 8: Formulate the problem for Gurobi
Given that we need to maximize $x_1x_2 + 9x_2^2 + 4x_1 + 3x_2$ subject to the constraints, and considering $x_1$ must be an integer and $x_2$ can be a real number, we should use Gurobi's Python API to model and solve this problem.

## 9: Write the Gurobi code
```python
import gurobi as gp

# Create a new model
m = gp.Model()

# Define variables
x1 = m.addVar(vtype=gp.GRB.INTEGER, name="milligrams of vitamin B3")
x2 = m.addVar(vtype=gp.GRB.CONTINUOUS, name="milligrams of calcium")

# Objective function
m.setObjective(x1*x2 + 9*x2**2 + 4*x1 + 3*x2, gp.GRB.MAXIMIZE)

# Constraints
m.addConstr(3*x1 == 3, name="muscle_growth_index_x1")
m.addConstr(x1 == 1, name="cardiovascular_support_index_x1")
m.addConstr(8*x1 == 8, name="digestive_support_index_x1")
m.addConstr(3*x2 == 3, name="muscle_growth_index_x2")
m.addConstr(4*x2 == 4, name="cardiovascular_support_index_x2")
m.addConstr(11*x2 == 11, name="digestive_support_index_x2")
m.addConstr(3*x1 + 3*x2 >= 20, name="total_muscle_growth_index")
m.addConstr(x1**2 + 16*x2**2 >= 56, name="total_cardiovascular_support_index")
m.addConstr(8*x1 + 11*x2 >= 61, name="total_digestive_support_index")
m.addConstr(6*x1**2 - 8*x2**2 >= 0, name="quadratic_constraint")
m.addConstr(3*x1 + 3*x2 <= 66, name="total_muscle_growth_index_upper_bound")
m.addConstr(x1**2 + 4*x2**2 <= 74, name="total_cardiovascular_support_index_upper_bound")
m.addConstr(8*x1 + 11*x2 <= 95, name="total_digestive_support_index_upper_bound")

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"x1: {x1.varValue}, x2: {x2.varValue}")
else:
    print("No optimal solution found.")
```

## 10: Symbolic representation
```json
{
    'sym_variables': [('x1', 'milligrams of vitamin B3'), ('x2', 'milligrams of calcium')],
    'objective_function': 'x1*x2 + 9*x2^2 + 4*x1 + 3*x2',
    'constraints': [
        '3*x1 = 3',
        'x1 = 1',
        '8*x1 = 8',
        '3*x2 = 3',
        '4*x2 = 4',
        '11*x2 = 11',
        '3*x1 + 3*x2 >= 20',
        'x1^2 + 16*x2^2 >= 56',
        '8*x1 + 11*x2 >= 61',
        '6*x1^2 - 8*x2^2 >= 0',
        '3*x1 + 3*x2 <= 66',
        'x1^2 + 4*x2^2 <= 74',
        '8*x1 + 11*x2 <= 95'
    ]
}
```