## Step 1: Define the symbolic representation of the variables
The variables are ['milligrams of vitamin A', 'milligrams of vitamin B1', 'milligrams of vitamin B2']. Let's denote them 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 A
- $x_1$ : milligrams of vitamin B1
- $x_2$ : milligrams of vitamin B2

## 3: Define the objective function in symbolic notation
The objective function to minimize is $9.2x_0^2 + 3.11x_0x_1 + 3.0x_2^2 + 4.71x_1 + 2.77x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
- $10x_0 = r0$ is not directly a constraint but $x_0$ has a muscle growth index of 10, implying $x_0 = 10$ for its index, not a constraint in the traditional sense but a given.
- $4x_0 = 4$ for cognitive performance index,
- $9x_1 = 9$ for muscle growth index,
- $12x_1 = 12$ for cognitive performance index,
- $4x_2 = 4$ for muscle growth index,
- $8x_2 = 8$ for cognitive performance index,
- $9x_1^2 + 4x_2^2 \geq 46$,
- $10x_0 + 4x_2 \geq 27$,
- $10x_0 + 9x_1 \geq 36$,
- $10x_0 + 9x_1 + 4x_2 \geq 36$,
- $4x_0 + 8x_2 \geq 14$,
- $12x_1 + 8x_2 \geq 6$,
- $4x_0 + 12x_1 + 8x_2 \geq 6$,
- $4x_0 - 4x_2 \geq 0$,
- $4x_0 + 12x_1 \leq 43$,
- $4x_0 + 8x_2 \leq 18$.

However, from the problem description, we see that $x_0 = 10$, $x_1 = 9$, and $x_2 = 4$ are given for their respective indices. These should be considered as part of the problem setup rather than traditional constraints to be optimized over.

## 5: Correctly interpret the given problem
Given that $x_0 = 10$, $x_1 = 9$, and $x_2 = 4$ based on their indices, let's reassess the problem. The actual optimization problem seems to be misinterpreted because the values of $x_0$, $x_1$, and $x_2$ are directly provided by their indices.

## 6: Formulate the problem with Gurobi
Given the specific values for $x_0$, $x_1$, and $x_2$ from their indices, the problem doesn't seem to require optimization over these variables as their values are determined. However, to follow through with an example of how one might set up an optimization problem with Gurobi for a similar problem, let's consider a general approach.

## 7: Symbolic Representation
```json
{
'sym_variables': [('x0', 'milligrams of vitamin A'), ('x1', 'milligrams of vitamin B1'), ('x2', 'milligrams of vitamin B2')],
'objective_function': '9.2x0^2 + 3.11x0*x1 + 3.0x2^2 + 4.71x1 + 2.77x2',
'constraints': [
    'x0 = 10',
    '4*x0 = 4',
    '9*x1 = 9',
    '12*x1 = 12',
    '4*x2 = 4',
    '8*x2 = 8',
    '9*x1^2 + 4*x2^2 >= 46',
    '10*x0 + 4*x2 >= 27',
    '10*x0 + 9*x1 >= 36',
    '10*x0 + 9*x1 + 4*x2 >= 36',
    '4*x0 + 8*x2 >= 14',
    '12*x1 + 8*x2 >= 6',
    '4*x0 + 12*x1 + 8*x2 >= 6',
    '4*x0 - 4*x2 >= 0',
    '4*x0 + 12*x1 <= 43',
    '4*x0 + 8*x2 <= 18'
]
}
```

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

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

# Define variables
x0 = m.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x0")
x1 = m.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x1")
x2 = m.addVar(lb=0, ub=gurobi.GRB.INFINITY, name="x2", vtype=gurobi.GRB.INTEGER)

# Objective function
m.setObjective(9.2*x0**2 + 3.11*x0*x1 + 3.0*x2**2 + 4.71*x1 + 2.77*x2, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(x0 == 10, name="c1")
m.addConstr(4*x0 == 4, name="c2")
m.addConstr(9*x1 == 9, name="c3")
m.addConstr(12*x1 == 12, name="c4")
m.addConstr(4*x2 == 4, name="c5")
m.addConstr(8*x2 == 8, name="c6")
m.addConstr(9*x1**2 + 4*x2**2 >= 46, name="c7")
m.addConstr(10*x0 + 4*x2 >= 27, name="c8")
m.addConstr(10*x0 + 9*x1 >= 36, name="c9")
m.addConstr(10*x0 + 9*x1 + 4*x2 >= 36, name="c10")
m.addConstr(4*x0 + 8*x2 >= 14, name="c11")
m.addConstr(12*x1 + 8*x2 >= 6, name="c12")
m.addConstr(4*x0 + 12*x1 + 8*x2 >= 6, name="c13")
m.addConstr(4*x0 - 4*x2 >= 0, name="c14")
m.addConstr(4*x0 + 12*x1 <= 43, name="c15")
m.addConstr(4*x0 + 8*x2 <= 18, name="c16")

# Optimize
m.optimize()

# Print solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objval)
    print("x0: ", x0.varValue)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
else:
    print("No solution found")
```