To solve this optimization problem, we first need to define the variables, objective function, and constraints using Gurobi's Python API.

## Step 1: Define the Variables
Let's define the variables for milligrams of calcium, vitamin B4, iron, vitamin B7, and vitamin B6.

## Step 2: Define the Objective Function
The objective function to maximize is: $9x_0 + 3x_1 + 5x_2 + 5x_3 + 1x_4$.

## Step 3: Define the Constraints
We have several constraints based on the problem description:
- $x_0 + 13x_1 + 3x_2 + 8x_3 + 11x_4 \leq 471$ (muscle growth index upper bound)
- $3x_0 + 5x_1 + 4x_2 + 10x_3 + 14x_4 \leq 163$ (energy stability index upper bound)
- $3x_2 + 8x_3 \geq 49$
- $13x_1 + 3x_2 + 8x_3 \geq 65$
- $x_0 + 13x_1 + 11x_4 \geq 65$
- $x_0 + 8x_3 + 11x_4 \geq 65$
- $13x_1 + 3x_2 + 8x_3 \geq 54$
- $x_0 + 13x_1 + 11x_4 \geq 54$
- $x_0 + 8x_3 + 11x_4 \geq 54$
- $13x_1 + 3x_2 + 8x_3 \geq 84$
- $x_0 + 13x_1 + 11x_4 \geq 84$
- $x_0 + 8x_3 + 11x_4 \geq 84$
- $4x_2 + 14x_4 \geq 27$
- $3x_0 + 10x_3 \geq 11$
- $3x_0 + 4x_2 \geq 24$
- $10x_3 + 14x_4 \geq 16$
- $5x_1 + 14x_4 \geq 16$
- $5x_2 - x_3 + 8x_4 \geq 0$
- $x_0 + 11x_4 \leq 398$
- $x_0 + 8x_3 \leq 262$
- $13x_1 + 3x_2 \leq 200$
- $3x_2 + 11x_4 \leq 469$
- $x_0 + 3x_2 \leq 350$
- $x_0 + 13x_1 \leq 426$
- $8x_3 + 11x_4 \leq 227$
- $13x_1 + 11x_4 \leq 194$
- $13x_1 + 8x_3 \leq 266$
- $x_0 + 13x_1 + 11x_4 \leq 187$
- $x_0 + 13x_1 + 3x_2 + 8x_3 + 11x_4 \leq 187$
- $4x_2 + 10x_3 \leq 111$
- $5x_1 + 4x_2 \leq 159$
- $5x_1 + 10x_3 \leq 84$
- $3x_0 + 5x_1 \leq 109$
- $5x_1 + 14x_4 \leq 157$
- $3x_0 + 10x_3 \leq 60$
- $3x_0 + 4x_2 \leq 42$
- $3x_0 + 5x_1 + 4x_2 \leq 79$
- $3x_0 + 10x_3 + 14x_4 \leq 103$
- $3x_0 + 5x_1 + 4x_2 + 10x_3 + 14x_4 \leq 103$

## Step 4: Implement in Gurobi
Here is the Gurobi code for the problem:

```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="calcium", lb=0)
    x1 = model.addVar(name="vitamin_B4", lb=0)
    x2 = model.addVar(name="iron", lb=0)
    x3 = model.addVar(name="vitamin_B7", lb=0)
    x4 = model.addVar(name="vitamin_B6", lb=0)

    # Objective function
    model.setObjective(9 * x0 + 3 * x1 + 5 * x2 + 5 * x3 + x4, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x0 + 13 * x1 + 3 * x2 + 8 * x3 + 11 * x4 <= 471)
    model.addConstr(3 * x0 + 5 * x1 + 4 * x2 + 10 * x3 + 14 * x4 <= 163)
    model.addConstr(3 * x2 + 8 * x3 >= 49)
    model.addConstr(13 * x1 + 3 * x2 + 8 * x3 >= 65)
    model.addConstr(x0 + 13 * x1 + 11 * x4 >= 65)
    model.addConstr(x0 + 8 * x3 + 11 * x4 >= 65)
    model.addConstr(13 * x1 + 3 * x2 + 8 * x3 >= 54)
    model.addConstr(x0 + 13 * x1 + 11 * x4 >= 54)
    model.addConstr(x0 + 8 * x3 + 11 * x4 >= 54)
    model.addConstr(13 * x1 + 3 * x2 + 8 * x3 >= 84)
    model.addConstr(x0 + 13 * x1 + 11 * x4 >= 84)
    model.addConstr(x0 + 8 * x3 + 11 * x4 >= 84)
    model.addConstr(4 * x2 + 14 * x4 >= 27)
    model.addConstr(3 * x0 + 10 * x3 >= 11)
    model.addConstr(3 * x0 + 4 * x2 >= 24)
    model.addConstr(10 * x3 + 14 * x4 >= 16)
    model.addConstr(5 * x1 + 14 * x4 >= 16)
    model.addConstr(5 * x2 - x3 + 8 * x4 >= 0)
    model.addConstr(x0 + 11 * x4 <= 398)
    model.addConstr(x0 + 8 * x3 <= 262)
    model.addConstr(13 * x1 + 3 * x2 <= 200)
    model.addConstr(3 * x2 + 11 * x4 <= 469)
    model.addConstr(x0 + 3 * x2 <= 350)
    model.addConstr(x0 + 13 * x1 <= 426)
    model.addConstr(8 * x3 + 11 * x4 <= 227)
    model.addConstr(13 * x1 + 11 * x4 <= 194)
    model.addConstr(13 * x1 + 8 * x3 <= 266)
    model.addConstr(x0 + 13 * x1 + 11 * x4 <= 187)
    model.addConstr(x0 + 13 * x1 + 3 * x2 + 8 * x3 + 11 * x4 <= 187)
    model.addConstr(4 * x2 + 10 * x3 <= 111)
    model.addConstr(5 * x1 + 4 * x2 <= 159)
    model.addConstr(5 * x1 + 10 * x3 <= 84)
    model.addConstr(3 * x0 + 5 * x1 <= 109)
    model.addConstr(5 * x1 + 14 * x4 <= 157)
    model.addConstr(3 * x0 + 10 * x3 <= 60)
    model.addConstr(3 * x0 + 4 * x2 <= 42)
    model.addConstr(3 * x0 + 5 * x1 + 4 * x2 <= 79)
    model.addConstr(3 * x0 + 10 * x3 + 14 * x4 <= 103)
    model.addConstr(3 * x0 + 5 * x1 + 4 * x2 + 10 * x3 + 14 * x4 <= 103)

    model.optimize()

    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Calcium: ", x0.varValue)
        print("Vitamin B4: ", x1.varValue)
        print("Iron: ", x2.varValue)
        print("Vitamin B7: ", x3.varValue)
        print("Vitamin B6: ", x4.varValue)
    else:
        print("No optimal solution found.")

optimize()
```