## Step 1: Define the symbolic representation of the variables
The variables are ['milligrams of calcium', 'milligrams of zinc', 'milligrams of vitamin C']. Let's denote them as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Define the symbolic representation of the problem
The objective function to maximize is $2.57x_1^2 + 9.67x_1x_2 + 5.9x_2^2 + 1.07x_3^2 + 5.17x_1$.

## Step 3: List all the constraints
- $x_1 \geq 0$ and $x_1$ is an integer (Implicitly handled by Gurobi's Var function with type=Integer)
- $x_2 \geq 0$
- $x_3 \geq 0$ and $x_3$ is an integer (Implicitly handled by Gurobi's Var function with type=Integer)
- $1x_1 + 3x_2 + 3x_3 \leq 50$
- $2x_1 + 8x_2 + 5x_3 \leq 106$
- $11x_1 + 11x_2 + 9x_3 \leq 81$
- $3x_2 + 3x_3 \geq 8$
- $1x_1 + 3x_3 \geq 10$
- $1x_1 + 3x_2 + 3x_3 \geq 15$
- $2x_1^2 + 8x_2^2 \geq 32$
- $11x_1^2 + 9x_3^2 \geq 13$
- $3x_2^2 + 3x_3^2 \leq 19$
- $1x_1 + 3x_2 \leq 40$
- $1x_1 + 3x_2 + 3x_3 \leq 40$
- $2x_1^2 + 8x_2^2 \leq 55$
- $2x_1^2 + 5x_3^2 \leq 79$
- $2x_1 + 8x_2 + 5x_3 \leq 79$
- $11x_1 + 9x_3 \leq 54$
- $11x_1 + 11x_2 + 9x_3 \leq 54$

## Step 4: Convert the problem into Gurobi code
```python
import gurobi

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

# Define the variables
x1 = m.addVar(name="milligrams_of_calcium", vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name="milligrams_of_zinc")
x3 = m.addVar(name="milligrams_of_vitamin_C", vtype=gurobi.GRB.INTEGER)

# Define the objective function
m.setObjective(2.57*x1**2 + 9.67*x1*x2 + 5.9*x2**2 + 1.07*x3**2 + 5.17*x1, gurobi.GRB.MAXIMIZE)

# Add constraints
m.addConstr(1*x1 + 3*x2 + 3*x3 <= 50, name="kidney_support_index")
m.addConstr(2*x1 + 8*x2 + 5*x3 <= 106, name="muscle_growth_index")
m.addConstr(11*x1 + 11*x2 + 9*x3 <= 81, name="cardiovascular_support_index")
m.addConstr(3*x2 + 3*x3 >= 8, name="kidney_support_index_zinc_vitamin_C")
m.addConstr(1*x1 + 3*x3 >= 10, name="kidney_support_index_calcium_vitamin_C")
m.addConstr(1*x1 + 3*x2 + 3*x3 >= 15, name="kidney_support_index_all")
m.addConstr(2*x1**2 + 8*x2**2 >= 32, name="muscle_growth_index_calcium_zinc")
m.addConstr(11*x1**2 + 9*x3**2 >= 13, name="cardiovascular_support_index_calcium_vitamin_C")
m.addConstr(3*x2**2 + 3*x3**2 <= 19, name="kidney_support_index_zinc_vitamin_C_squared")
m.addConstr(1*x1 + 3*x2 <= 40, name="kidney_support_index_calcium_zinc")
m.addConstr(1*x1 + 3*x2 + 3*x3 <= 40, name="kidney_support_index_all_equal")
m.addConstr(2*x1**2 + 8*x2**2 <= 55, name="muscle_growth_index_calcium_zinc_squared")
m.addConstr(2*x1**2 + 5*x3**2 <= 79, name="muscle_growth_index_calcium_vitamin_C_squared")
m.addConstr(2*x1 + 8*x2 + 5*x3 <= 79, name="muscle_growth_index_all")
m.addConstr(11*x1 + 9*x3 <= 54, name="cardiovascular_support_index_calcium_vitamin_C_linear")
m.addConstr(11*x1 + 11*x2 + 9*x3 <= 54, name="cardiovascular_support_index_all")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print("Milligrams of calcium: ", x1.varValue)
    print("Milligrams of zinc: ", x2.varValue)
    print("Milligrams of vitamin C: ", x3.varValue)
    print("Objective function value: ", m.objVal)
else:
    print("No optimal solution found.")
```

## Step 5: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'milligrams of calcium'), 
        ('x2', 'milligrams of zinc'), 
        ('x3', 'milligrams of vitamin C')
    ], 
    'objective_function': '2.57*x1^2 + 9.67*x1*x2 + 5.9*x2^2 + 1.07*x3^2 + 5.17*x1', 
    'constraints': [
        '1*x1 + 3*x2 + 3*x3 <= 50', 
        '2*x1 + 8*x2 + 5*x3 <= 106', 
        '11*x1 + 11*x2 + 9*x3 <= 81', 
        '3*x2 + 3*x3 >= 8', 
        '1*x1 + 3*x3 >= 10', 
        '1*x1 + 3*x2 + 3*x3 >= 15', 
        '2*x1^2 + 8*x2^2 >= 32', 
        '11*x1^2 + 9*x3^2 >= 13', 
        '3*x2^2 + 3*x3^2 <= 19', 
        '1*x1 + 3*x2 <= 40', 
        '1*x1 + 3*x2 + 3*x3 <= 40', 
        '2*x1^2 + 8*x2^2 <= 55', 
        '2*x1^2 + 5*x3^2 <= 79', 
        '2*x1 + 8*x2 + 5*x3 <= 79', 
        '11*x1 + 9*x3 <= 54', 
        '11*x1 + 11*x2 + 9*x3 <= 54'
    ]
}
```