## Step 1: Define the optimization problem and its components
The problem requires minimizing an objective function with three variables: $x_0$ (grams of fat), $x_1$ (milligrams of vitamin B3), and $x_2$ (grams of fiber). The objective function to minimize is $6x_0^2 + 3x_0x_1 + 8x_0x_2 + 4x_1^2 + 3x_1x_2 + 9x_2^2 + 8x_0 + 8x_1 + 8x_2$.

## 2: Identify the constraints
The constraints given are:
- $2x_0 + 8x_1 + 8x_2 \geq 14$ (cardiovascular support index constraint)
- $5x_0 + 4x_1 + x_2 \geq 7$ (muscle growth index constraint)
- $4x_1^2 + x_2^2 \geq 5$ (muscle growth index constraint from squared terms)
- $5x_0^2 + x_2^2 \geq 7$ (muscle growth index constraint from squared terms)
- $5x_0 + 4x_1 + x_2 \geq 7$ (muscle growth index constraint, already considered)
- $7x_0 - 5x_2 \geq 0$ (additional constraint)
- $x_0, x_1, x_2$ can be fractional.

## 3: Express the problem in a standard form for Gurobi
To solve this problem using Gurobi, we need to express it in a standard form. However, Gurobi directly supports quadratic objective functions and constraints, making it suitable for this problem.

## 4: Write the Gurobi code
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(lb=-gurobi.GRB.INFINITY, name="grams_of_fat", vtype=gurobi.GRB.CONTINUOUS)
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, name="milligrams_of_vitamin_B3", vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, name="grams_of_fiber", vtype=gurobi.GRB.CONTINUOUS)

    # Objective function
    model.setObjective(6*x0**2 + 3*x0*x1 + 8*x0*x2 + 4*x1**2 + 3*x1*x2 + 9*x2**2 + 8*x0 + 8*x1 + 8*x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(2*x0 + 8*x1 + 8*x2 >= 14, name="cardiovascular_support_index")
    model.addConstr(5*x0 + 4*x1 + x2 >= 7, name="muscle_growth_index")
    model.addConstr(4*x1**2 + x2**2 >= 5, name="muscle_growth_index_squared_terms_1")
    model.addConstr(5*x0**2 + x2**2 >= 7, name="muscle_growth_index_squared_terms_2")
    model.addConstr(5*x0 + 4*x1 + x2 >= 7, name="muscle_growth_index_2") # This is a repeat, consider removing
    model.addConstr(7*x0 - 5*x2 >= 0, name="additional_constraint")

    # Remove duplicate constraint
    # model.remove(model.getConstrByName("muscle_growth_index_2"))

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Grams of fat: ", x0.varValue)
        print("Milligrams of vitamin B3: ", x1.varValue)
        print("Grams of fiber: ", x2.varValue)
    else:
        print("No optimal solution found")

solve_optimization_problem()
```

The final answer is: 
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(lb=-gurobi.GRB.INFINITY, name="grams_of_fat", vtype=gurobi.GRB.CONTINUOUS)
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, name="milligrams_of_vitamin_B3", vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, name="grams_of_fiber", vtype=gurobi.GRB.CONTINUOUS)

    # Objective function
    model.setObjective(6*x0**2 + 3*x0*x1 + 8*x0*x2 + 4*x1**2 + 3*x1*x2 + 9*x2**2 + 8*x0 + 8*x1 + 8*x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(2*x0 + 8*x1 + 8*x2 >= 14, name="cardiovascular_support_index")
    model.addConstr(5*x0 + 4*x1 + x2 >= 7, name="muscle_growth_index")
    model.addConstr(4*x1**2 + x2**2 >= 5, name="muscle_growth_index_squared_terms_1")
    model.addConstr(5*x0**2 + x2**2 >= 7, name="muscle_growth_index_squared_terms_2")
    model.addConstr(7*x0 - 5*x2 >= 0, name="additional_constraint")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Grams of fat: ", x0.varValue)
        print("Milligrams of vitamin B3: ", x1.varValue)
        print("Grams of fiber: ", x2.varValue)
    else:
        print("No optimal solution found")

solve_optimization_problem()
```