## Step 1: Define the symbolic representation of the variables
The variables are 'milligrams of iron', 'milligrams of vitamin B3', and 'milligrams of vitamin B2', which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the natural language description into a symbolic representation
The symbolic representation of the variables is:
- $x_0$ : milligrams of iron
- $x_1$ : milligrams of vitamin B3
- $x_2$ : milligrams of vitamin B2

## 3: Define the objective function in symbolic notation
The objective function to maximize is $3x_0x_1 + 7x_0x_2 + 7x_2^2 + 6x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
- $6x_0 \leq 90$ (cognitive performance index for $x_0$)
- $22x_0 \leq 130$ (muscle growth index for $x_0$)
- $15x_1 \leq 90$ (cognitive performance index for $x_1$)
- $6x_1 \leq 130$ (muscle growth index for $x_1$)
- $13x_2 \leq 90$ (cognitive performance index for $x_2$)
- $20x_2 \leq 130$ (muscle growth index for $x_2$)
- $22^2x_0^2 + 20^2x_2^2 \geq 40$ (total combined muscle growth index from $x_0^2$ and $x_2^2$)
- $6x_1 + 20x_2 \geq 42$ (total combined muscle growth index from $x_1$ and $x_2$)
- $15x_1 + 13x_2 \leq 46$ (total combined cognitive performance index from $x_1$ and $x_2$)
- $6^2x_0^2 + 15^2x_1^2 \leq 79$ (total combined cognitive performance index from $x_0^2$ and $x_1^2$)
- $6x_0 + 15x_1 + 13x_2 \leq 79$ (total combined cognitive performance index from $x_0$, $x_1$, and $x_2$)
- $6^2x_1^2 + 20^2x_2^2 \leq 79$ (total combined muscle growth index from $x_1^2$ and $x_2^2$)
- $22^2x_0^2 + 6^2x_1^2 \leq 126$ (total combined muscle growth index from $x_0^2$ and $x_1^2$)
- $22x_0 + 6x_1 + 20x_2 \leq 49$ (total combined muscle growth index from $x_0$, $x_1$, and $x_2$)
- $x_0$ is an integer
- $x_2$ is an integer

## 5: Provide the symbolic representation in the required format
```json
{
    'sym_variables': [
        ('x0', 'milligrams of iron'), 
        ('x1', 'milligrams of vitamin B3'), 
        ('x2', 'milligrams of vitamin B2')
    ], 
    'objective_function': '3*x0*x1 + 7*x0*x2 + 7*x2^2 + 6*x2', 
    'constraints': [
        '6*x0 <= 90', 
        '22*x0 <= 130', 
        '15*x1 <= 90', 
        '6*x1 <= 130', 
        '13*x2 <= 90', 
        '20*x2 <= 130', 
        '484*x0^2 + 400*x2^2 >= 40', 
        '6*x1 + 20*x2 >= 42', 
        '15*x1 + 13*x2 <= 46', 
        '36*x0^2 + 225*x1^2 <= 79', 
        '6*x0 + 15*x1 + 13*x2 <= 79', 
        '36*x1^2 + 400*x2^2 <= 79', 
        '484*x0^2 + 36*x1^2 <= 126', 
        '22*x0 + 6*x1 + 20*x2 <= 49'
    ]
}
```

## 6: Implement the optimization problem using Gurobi
```python
import gurobi

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

# Define the variables
x0 = model.addVar(name="x0", vtype=gurobi.GRB.INTEGER)  # milligrams of iron
x1 = model.addVar(name="x1")  # milligrams of vitamin B3
x2 = model.addVar(name="x2", vtype=gurobi.GRB.INTEGER)  # milligrams of vitamin B2

# Objective function
model.setObjective(3*x0*x1 + 7*x0*x2 + 7*x2**2 + 6*x2, gurobi.GRB.MAXIMIZE)

# Constraints
model.addConstr(6*x0 <= 90)
model.addConstr(22*x0 <= 130)
model.addConstr(15*x1 <= 90)
model.addConstr(6*x1 <= 130)
model.addConstr(13*x2 <= 90)
model.addConstr(20*x2 <= 130)
model.addConstr(484*x0**2 + 400*x2**2 >= 40)
model.addConstr(6*x1 + 20*x2 >= 42)
model.addConstr(15*x1 + 13*x2 <= 46)
model.addConstr(36*x0**2 + 225*x1**2 <= 79)
model.addConstr(6*x0 + 15*x1 + 13*x2 <= 79)
model.addConstr(36*x1**2 + 400*x2**2 <= 79)
model.addConstr(484*x0**2 + 36*x1**2 <= 126)
model.addConstr(22*x0 + 6*x1 + 20*x2 <= 49)

# Solve the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Milligrams of iron: {x0.varValue}")
    print(f"Milligrams of vitamin B3: {x1.varValue}")
    print(f"Milligrams of vitamin B2: {x2.varValue}")
    print(f"Objective function value: {model.objVal}")
else:
    print("No optimal solution found.")
```