## Step 1: Define the symbolic representation of the variables
The variables are defined as follows: 
- $x_0$ represents 'grams of carbohydrates'
- $x_1$ represents 'milligrams of vitamin D'
- $x_2$ represents 'milligrams of zinc'
- $x_3$ represents 'grams of protein'

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $5x_0 + 2x_1 + 6x_2 + 8x_3$.

## Step 3: Define the constraints in symbolic notation
The constraints are as follows:
- $8x_0 \leq 181$ (digestive support index for $x_0$)
- $11x_0 \leq 152$ (muscle growth index for $x_0$)
- $10x_1 \leq 181$ (digestive support index for $x_1$)
- $9x_1 \leq 152$ (muscle growth index for $x_1$)
- $7x_2 \leq 181$ (digestive support index for $x_2$)
- $5x_2 \leq 152$ (muscle growth index for $x_2$)
- $10x_3 \leq 181$ (digestive support index for $x_3$)
- $4x_3 \leq 152$ (muscle growth index for $x_3$)
- $8x_0 + 10x_1 \geq 26$ 
- $8x_0 + 7x_2 + 10x_3 \geq 35$
- $10x_1 + 7x_2 + 10x_3 \geq 35$
- $8x_0 + 7x_2 + 10x_3 \geq 35$ (same as above)
- $10x_1 + 7x_2 + 10x_3 \geq 35$ (same as above)
- $8x_0 + 10x_1 + 7x_2 + 10x_3 \geq 35$
- $11x_0 + 5x_2 \geq 25$
- $11x_0 + 4x_3 \geq 14$
- $11x_0 + 9x_1 + 5x_2 + 4x_3 \geq 14$
- $-8x_1 + 6x_3 \geq 0$
- $-4x_0 + 6x_1 \geq 0$
- $8x_0 + 10x_1 + 7x_2 \leq 94$
- $10x_1 + 7x_2 + 10x_3 \leq 144$
- $9x_1 + 4x_3 \leq 89$
- $9x_1 + 5x_2 \leq 81$
- $11x_0 + 9x_1 + 5x_2 \leq 60$

## 4: Write down the problem in json format

```json
{
    'sym_variables': [
        ('x0', 'grams of carbohydrates'), 
        ('x1', 'milligrams of vitamin D'), 
        ('x2', 'milligrams of zinc'), 
        ('x3', 'grams of protein')
    ], 
    'objective_function': '5*x0 + 2*x1 + 6*x2 + 8*x3', 
    'constraints': [
        '8*x0 <= 181', 
        '11*x0 <= 152', 
        '10*x1 <= 181', 
        '9*x1 <= 152', 
        '7*x2 <= 181', 
        '5*x2 <= 152', 
        '10*x3 <= 181', 
        '4*x3 <= 152', 
        '8*x0 + 10*x1 >= 26', 
        '8*x0 + 7*x2 + 10*x3 >= 35', 
        '10*x1 + 7*x2 + 10*x3 >= 35', 
        '8*x0 + 7*x2 + 10*x3 >= 35', 
        '10*x1 + 7*x2 + 10*x3 >= 35', 
        '8*x0 + 10*x1 + 7*x2 + 10*x3 >= 35', 
        '11*x0 + 5*x2 >= 25', 
        '11*x0 + 4*x3 >= 14', 
        '11*x0 + 9*x1 + 5*x2 + 4*x3 >= 14', 
        '-8*x1 + 6*x3 >= 0', 
        '-4*x0 + 6*x1 >= 0', 
        '8*x0 + 10*x1 + 7*x2 <= 94', 
        '10*x1 + 7*x2 + 10*x3 <= 144', 
        '9*x1 + 4*x3 <= 89', 
        '9*x1 + 5*x2 <= 81', 
        '11*x0 + 9*x1 + 5*x2 <= 60'
    ]
}
```

## 5: Implement the optimization problem using Gurobi

```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name="x0", lb=0) # grams of carbohydrates
    x1 = model.addVar(name="x1", lb=0) # milligrams of vitamin D
    x2 = model.addVar(name="x2", lb=0) # milligrams of zinc
    x3 = model.addVar(name="x3", lb=0) # grams of protein

    # Objective function
    model.setObjective(5*x0 + 2*x1 + 6*x2 + 8*x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(8*x0 <= 181)
    model.addConstr(11*x0 <= 152)
    model.addConstr(10*x1 <= 181)
    model.addConstr(9*x1 <= 152)
    model.addConstr(7*x2 <= 181)
    model.addConstr(5*x2 <= 152)
    model.addConstr(10*x3 <= 181)
    model.addConstr(4*x3 <= 152)
    model.addConstr(8*x0 + 10*x1 >= 26)
    model.addConstr(8*x0 + 7*x2 + 10*x3 >= 35)
    model.addConstr(10*x1 + 7*x2 + 10*x3 >= 35)
    model.addConstr(8*x0 + 7*x2 + 10*x3 >= 35)
    model.addConstr(10*x1 + 7*x2 + 10*x3 >= 35)
    model.addConstr(8*x0 + 10*x1 + 7*x2 + 10*x3 >= 35)
    model.addConstr(11*x0 + 5*x2 >= 25)
    model.addConstr(11*x0 + 4*x3 >= 14)
    model.addConstr(11*x0 + 9*x1 + 5*x2 + 4*x3 >= 14)
    model.addConstr(-8*x1 + 6*x3 >= 0)
    model.addConstr(-4*x0 + 6*x1 >= 0)
    model.addConstr(8*x0 + 10*x1 + 7*x2 <= 94)
    model.addConstr(10*x1 + 7*x2 + 10*x3 <= 144)
    model.addConstr(9*x1 + 4*x3 <= 89)
    model.addConstr(9*x1 + 5*x2 <= 81)
    model.addConstr(11*x0 + 9*x1 + 5*x2 <= 60)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("x0: ", x0.varValue)
        print("x1: ", x1.varValue)
        print("x2: ", x2.varValue)
        print("x3: ", x3.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```