## Step 1: Define the symbolic representation of the variables
The variables are 'grams of carbohydrates' and 'milligrams of vitamin B6'. Let's denote 'grams of carbohydrates' as $x_1$ and 'milligrams of vitamin B6' as $x_2$.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $6.63x_1^2 + 7.63x_1x_2 + 4.72x_2^2 + 3.6x_1 + 8.16x_2$.

## 3: Define the constraints in symbolic notation
The constraints are:
- $x_1$ has a cognitive performance index of 1: $1x_1$
- $x_1$ has a kidney support index of 2: $2x_1$
- $x_2$ has a cognitive performance index of 6: $6x_2$
- $x_2$ has a kidney support index of 1: $1x_2$
- The total combined cognitive performance index from $x_1$ and $x_2$ squared must be greater than or equal to 32: $x_1^2 + 6^2x_2^2 \geq 32$ or simply $x_1^2 + 36x_2^2 \geq 32$
- The total combined kidney support index from $x_1$ and $x_2$ squared has to be as much or more than 33: $2^2x_1^2 + 1^2x_2^2 \geq 33$ or simply $4x_1^2 + x_2^2 \geq 33$
- $8x_1 - 7x_2 \geq 0$
- The total combined cognitive performance index from $x_1$ and $x_2$ has to be 78 or less: $x_1 + 6x_2 \leq 78$
- The total combined kidney support index from $x_1$ and $x_2$ must be 54 at a maximum: $2x_1 + x_2 \leq 54$
- $x_2$ must be an integer.

## 4: Correcting and Clarifying Constraints
Correcting the interpretation of constraints:
- Cognitive performance index constraint: $x_1 + 6x_2 \leq 90$ (from $r0$)
- Kidney support index constraint: $2x_1 + x_2 \leq 77$ (from $r1$)
- And the squared terms constraints are correctly identified but let's ensure they match the problem statement.

## 5: Symbolic Representation
The symbolic representation is:
- Variables: $x_1$ for 'grams of carbohydrates', $x_2$ for 'milligrams of vitamin B6'
- Objective function: $6.63x_1^2 + 7.63x_1x_2 + 4.72x_2^2 + 3.6x_1 + 8.16x_2$
- Constraints:
  1. $x_1^2 + 36x_2^2 \geq 32$
  2. $4x_1^2 + x_2^2 \geq 33$
  3. $8x_1 - 7x_2 \geq 0$
  4. $x_1 + 6x_2 \leq 78$
  5. $2x_1 + x_2 \leq 54$
  6. $x_1 \leq 90$ (cognitive performance index upper bound for $x_1$)
  7. $2x_1 \leq 77$ (kidney support index upper bound for $x_1$)
  8. $6x_2 \leq 90$ (cognitive performance index upper bound for $x_2$)
  9. $x_2 \leq 77$ (kidney support index upper bound for $x_2$, but directly from $r1$ it's $x_2$)

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

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

# Define variables
x1 = m.addVar(name="carbohydrates", vtype=gurobi.GRB.CONTINUOUS)
x2 = m.addVar(name="vitamin_B6", vtype=gurobi.GRB.INTEGER)

# Objective function
m.setObjective(6.63*x1**2 + 7.63*x1*x2 + 4.72*x2**2 + 3.6*x1 + 8.16*x2, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(x1**2 + 36*x2**2 >= 32, name="cognitive_performance_squared")
m.addConstr(4*x1**2 + x2**2 >= 33, name="kidney_support_squared")
m.addConstr(8*x1 - 7*x2 >= 0, name="carbohydrates_vitamin_B6_relation")
m.addConstr(x1 + 6*x2 <= 78, name="total_cognitive_performance")
m.addConstr(2*x1 + x2 <= 54, name="total_kidney_support")
m.addConstr(x1 <= 90, name="carbohydrates_cognitive_performance_limit")
m.addConstr(2*x1 <= 77, name="carbohydrates_kidney_support_limit")

# Optimize
m.optimize()

# Print solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Carbohydrates: {x1.varValue}")
    print(f"Vitamin B6: {x2.varValue}")
    print(f"Objective: {m.objVal}")
else:
    print("No optimal solution found.")
```

## 7: Final Output
```json
{
    'sym_variables': [('x1', 'grams of carbohydrates'), ('x2', 'milligrams of vitamin B6')],
    'objective_function': '6.63x1^2 + 7.63x1x2 + 4.72x2^2 + 3.6x1 + 8.16x2',
    'constraints': [
        'x1^2 + 36x2^2 >= 32',
        '4x1^2 + x2^2 >= 33',
        '8x1 - 7x2 >= 0',
        'x1 + 6x2 <= 78',
        '2x1 + x2 <= 54'
    ]
}
```