## Step 1: Define the symbolic representation of the variables
The variables are ['milligrams of vitamin K', 'milligrams of vitamin B5', 'milligrams of vitamin A'] which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the natural language objects into symbolic notation
The symbolic representation of the variables is:
- $x_0$ : milligrams of vitamin K
- $x_1$ : milligrams of vitamin B5
- $x_2$ : milligrams of vitamin A

## 3: Define the objective function in symbolic notation
The objective function to maximize is $3x_0x_1 + 3x_1^2 + 2x_1 + 3x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
- $5x_0 = 5$
- $17x_0 = 17$
- $14x_0 = 14$
- $10x_0 = 10$
- $4x_1 = 4$
- $10x_1 = 10$
- $17x_1 = 17$
- $16x_1 = 16$
- $14x_2 = 14$
- $5x_2 = 5$
- $4x_2 = 4$
- $6x_2 = 6$
- $4x_1 + 14x_2 \geq 42$
- $5x_0 + 14x_2 \geq 38$
- $5x_0 + 4x_1 + 14x_2 \geq 32$
- $17^2x_0^2 + 5^2x_2^2 \geq 30$
- $14^2x_0^2 + 17^2x_1^2 + 4^2x_2^2 \geq 27$
- $10x_0 + 16x_1 + 6x_2 \geq 59$
- $4x_1 + 14x_2 \leq 70$
- $5x_0 + 4x_1 + 14x_2 \leq 70$
- $10^2x_1^2 + 5^2x_2^2 \leq 105$
- $17x_0 + 10x_1 \leq 121$
- $17x_0 + 10x_1 + 5x_2 \leq 121$
- $14x_0 + 17x_1 \leq 68$
- $14x_0 + 4x_2 \leq 72$
- $14x_0 + 17x_1 + 4x_2 \leq 72$
- $10x_0 + 6x_2 \leq 85$
- $10x_0 + 16x_1 \leq 102$
- $10x_0 + 16x_1 + 6x_2 \leq 102$

## 5: Simplify the constraints
From the constraints $5x_0 = 5$, $17x_0 = 17$, $14x_0 = 14$, and $10x_0 = 10$, we can directly deduce that $x_0 = 1$.

From the constraints $4x_1 = 4$, $10x_1 = 10$, $17x_1 = 17$, and $16x_1 = 16$, we can directly deduce that $x_1 = 1$.

From the constraints $14x_2 = 14$, $5x_2 = 5$, $4x_2 = 4$, and $6x_2 = 6$, we can directly deduce that $x_2 = 1$.

## 6: Verify if the direct deductions satisfy all constraints
Given $x_0 = 1$, $x_1 = 1$, and $x_2 = 1$, let's verify if these satisfy all constraints:
- Cognitive performance index: $5*1 + 4*1 + 14*1 = 5 + 4 + 14 = 23$
- Kidney support index: $17*1 + 10*1 + 5*1 = 17 + 10 + 5 = 32$
- Cardiovascular support index: $14*1 + 17*1 + 4*1 = 14 + 17 + 4 = 35$
- Immune support index: $10*1 + 16*1 + 6*1 = 10 + 16 + 6 = 32$

## 7: Check the objective function and constraints with the given values
The objective function becomes $3*1*1 + 3*1^2 + 2*1 + 3*1 = 3 + 3 + 2 + 3 = 11$.

## 8: Implement the problem in Gurobi
Given that we have directly deduced $x_0 = 1$, $x_1 = 1$, and $x_2 = 1$ from the equality constraints, and these values seem to straightforwardly satisfy the given equalities, we should confirm if they indeed optimize the given problem under all constraints.

```python
import gurobipy as gp

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

# Define variables
x0 = m.addVar(name="x0", lb=0)  # milligrams of vitamin K
x1 = m.addVar(name="x1", lb=0)  # milligrams of vitamin B5
x2 = m.addVar(name="x2", lb=0)  # milligrams of vitamin A

# Objective function
m.setObjective(3*x0*x1 + 3*x1**2 + 2*x1 + 3*x2, gp.GRB.MAXIMIZE)

# Constraints
m.addConstr(5*x0 == 5)
m.addConstr(17*x0 == 17)
m.addConstr(14*x0 == 14)
m.addConstr(10*x0 == 10)

m.addConstr(4*x1 == 4)
m.addConstr(10*x1 == 10)
m.addConstr(17*x1 == 17)
m.addConstr(16*x1 == 16)

m.addConstr(14*x2 == 14)
m.addConstr(5*x2 == 5)
m.addConstr(4*x2 == 4)
m.addConstr(6*x2 == 6)

m.addConstr(4*x1 + 14*x2 >= 42)
m.addConstr(5*x0 + 14*x2 >= 38)
m.addConstr(5*x0 + 4*x1 + 14*x2 >= 32)
m.addConstr(17**2*x0**2 + 5**2*x2**2 >= 30)
m.addConstr(14**2*x0**2 + 17**2*x1**2 + 4**2*x2**2 >= 27)
m.addConstr(10*x0 + 16*x1 + 6*x2 >= 59)
m.addConstr(4*x1 + 14*x2 <= 70)
m.addConstr(5*x0 + 4*x1 + 14*x2 <= 70)
m.addConstr(10**2*x1**2 + 5**2*x2**2 <= 105)
m.addConstr(17*x0 + 10*x1 <= 121)
m.addConstr(17*x0 + 10*x1 + 5*x2 <= 121)
m.addConstr(14*x0 + 17*x1 <= 68)
m.addConstr(14*x0 + 4*x2 <= 72)
m.addConstr(14*x0 + 17*x1 + 4*x2 <= 72)
m.addConstr(10*x0 + 6*x2 <= 85)
m.addConstr(10*x0 + 16*x1 <= 102)
m.addConstr(10*x0 + 16*x1 + 6*x2 <= 102)

# Solve the model
m.optimize()

# Print the solution
print("Objective: ", m.objVal)
print("x0: ", x0.varValue)
print("x1: ", x1.varValue)
print("x2: ", x2.varValue)
```

## 9: Symbolic Representation
```json
{
    'sym_variables': [('x0', 'milligrams of vitamin K'), ('x1', 'milligrams of vitamin B5'), ('x2', 'milligrams of vitamin A')],
    'objective_function': '3*x0*x1 + 3*x1^2 + 2*x1 + 3*x2',
    'constraints': [
        '5*x0 = 5',
        '17*x0 = 17',
        '14*x0 = 14',
        '10*x0 = 10',
        '4*x1 = 4',
        '10*x1 = 10',
        '17*x1 = 17',
        '16*x1 = 16',
        '14*x2 = 14',
        '5*x2 = 5',
        '4*x2 = 4',
        '6*x2 = 6',
        '4*x1 + 14*x2 >= 42',
        '5*x0 + 14*x2 >= 38',
        '5*x0 + 4*x1 + 14*x2 >= 32',
        '17^2*x0^2 + 5^2*x2^2 >= 30',
        '14^2*x0^2 + 17^2*x1^2 + 4^2*x2^2 >= 27',
        '10*x0 + 16*x1 + 6*x2 >= 59',
        '4*x1 + 14*x2 <= 70',
        '5*x0 + 4*x1 + 14*x2 <= 70',
        '10^2*x1^2 + 5^2*x2^2 <= 105',
        '17*x0 + 10*x1 <= 121',
        '17*x0 + 10*x1 + 5*x2 <= 121',
        '14*x0 + 17*x1 <= 68',
        '14*x0 + 4*x2 <= 72',
        '14*x0 + 17*x1 + 4*x2 <= 72',
        '10*x0 + 6*x2 <= 85',
        '10*x0 + 16*x1 <= 102',
        '10*x0 + 16*x1 + 6*x2 <= 102'
    ]
}
```