## Step 1: Define the symbolic representation of the variables
The variables are ['milligrams of vitamin B7', 'grams of carbohydrates', 'milligrams of vitamin B5']. 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 B7
- $x_1$ : grams of carbohydrates
- $x_2$ : milligrams of vitamin B5

## 3: Define the objective function in symbolic notation
The objective function to maximize is: $8.64x_0^2 + 6.6x_1^2 + 7.34x_1x_2 + 2.91x_1 + 2.27x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
- $12x_0 \leq 157$ ( muscle growth index for $x_0$ is 12, and its upper bound is 157, but this seems to be an upper bound for $x_0$ itself: $x_0 \leq 157/12$)
- $10x_0 \leq 77$ (digestive support index for $x_0$)
- $6x_1 \leq 157$ (muscle growth index for $x_1$)
- $15x_1 \leq 77$ (digestive support index for $x_1$)
- $15x_2 \leq 157$ (muscle growth index for $x_2$)
- $14x_2 \leq 77$ (digestive support index for $x_2$)
- $6x_1 + 15x_2 \leq 108$ (total combined muscle growth index from $x_1$ and $x_2$)
- $12^2x_0^2 + 6^2x_1^2 \leq 138$ (total combined muscle growth index from $x_0^2$ and $x_1^2$)
- $12x_0 + 15x_2 \leq 117$ (total combined muscle growth index from $x_0$ and $x_2$)
- $12^2x_0^2 + 6^2x_1^2 + 15^2x_2^2 \leq 78$ (total combined muscle growth index from $x_0^2$, $x_1^2$, and $x_2^2$)
- $12x_0 + 6x_1 + 15x_2 \leq 78$ (total combined muscle growth index from $x_0$, $x_1$, and $x_2$)
- $15x_1 + 14x_2 \leq 61$ (total combined digestive support index from $x_1$ and $x_2$)
- $10^2x_0^2 + 14^2x_2^2 \leq 30$ (total combined digestive support index from $x_0^2$ and $x_2^2$)
- $10^2x_0^2 + 15^2x_1^2 + 14^2x_2^2 \leq 26$ (total combined digestive support index from $x_0^2$, $x_1^2$, and $x_2^2$)
- $10x_0 + 15x_1 + 14x_2 \leq 26$ (total combined digestive support index from $x_0$, $x_1$, and $x_2$)

## 5: Correct and simplify constraints based on problem description
Correcting and simplifying:
- $x_0 \leq 157/12$
- $10x_0 \leq 77$
- The actual constraints from the problem statement should directly use $r0$ and $r1$ values:
  - $12x_0 \leq 157$
  - $10x_0 \leq 77$
  - $6x_1 \leq 157$
  - $15x_1 \leq 77$
  - $15x_2 \leq 157$
  - $14x_2 \leq 77$
  - $6x_1 + 15x_2 \leq 108$
  - $144x_0^2 + 36x_1^2 \leq 138$
  - $12x_0 + 15x_2 \leq 117$
  - $144x_0^2 + 36x_1^2 + 225x_2^2 \leq 78$
  - $12x_0 + 6x_1 + 15x_2 \leq 78$
  - $15x_1 + 14x_2 \leq 61$
  - $100x_0^2 + 196x_2^2 \leq 30$
  - $100x_0^2 + 225x_1^2 + 196x_2^2 \leq 26$
  - $10x_0 + 15x_1 + 14x_2 \leq 26$

## 6: Write down the symbolic representation
```json
{
    'sym_variables': [('x0', 'milligrams of vitamin B7'), ('x1', 'grams of carbohydrates'), ('x2', 'milligrams of vitamin B5')],
    'objective_function': '8.64*x0^2 + 6.6*x1^2 + 7.34*x1*x2 + 2.91*x1 + 2.27*x2',
    'constraints': [
        'x0 <= 157/12',
        '10*x0 <= 77',
        '6*x1 <= 157',
        '15*x1 <= 77',
        '15*x2 <= 157',
        '14*x2 <= 77',
        '6*x1 + 15*x2 <= 108',
        '144*x0^2 + 36*x1^2 <= 138',
        '12*x0 + 15*x2 <= 117',
        '144*x0^2 + 36*x1^2 + 225*x2^2 <= 78',
        '12*x0 + 6*x1 + 15*x2 <= 78',
        '15*x1 + 14*x2 <= 61',
        '100*x0^2 + 196*x2^2 <= 30',
        '100*x0^2 + 225*x1^2 + 196*x2^2 <= 26',
        '10*x0 + 15*x1 + 14*x2 <= 26'
    ]
}
```

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

def optimize_problem():
    model = gurobi.Model()
    
    # Define variables
    x0 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x0")
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x1")
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x2")
    
    # Objective function
    model.setObjective(8.64*x0**2 + 6.6*x1**2 + 7.34*x1*x2 + 2.91*x1 + 2.27*x2, gurobi.GRB.MAXIMIZE)
    
    # Constraints
    model.addConstr(x0 <= 157/12)
    model.addConstr(10*x0 <= 77)
    model.addConstr(6*x1 <= 157)
    model.addConstr(15*x1 <= 77)
    model.addConstr(15*x2 <= 157)
    model.addConstr(14*x2 <= 77)
    model.addConstr(6*x1 + 15*x2 <= 108)
    model.addConstr(144*x0**2 + 36*x1**2 <= 138)
    model.addConstr(12*x0 + 15*x2 <= 117)
    model.addConstr(144*x0**2 + 36*x1**2 + 225*x2**2 <= 78)
    model.addConstr(12*x0 + 6*x1 + 15*x2 <= 78)
    model.addConstr(15*x1 + 14*x2 <= 61)
    model.addConstr(100*x0**2 + 196*x2**2 <= 30)
    model.addConstr(100*x0**2 + 225*x1**2 + 196*x2**2 <= 26)
    model.addConstr(10*x0 + 15*x1 + 14*x2 <= 26)
    
    # Solve the model
    model.optimize()
    
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Optimal solution found.")
        print(f"x0: {x0.varValue}")
        print(f"x1: {x1.varValue}")
        print(f"x2: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

optimize_problem()
```