## Step 1: Define the optimization problem
The problem is to minimize the objective function: $7z + 5r_2 + 4r_4 + 7r_C$, where $z$ represents milligrams of zinc, $r_2$ represents milligrams of vitamin B2, $r_4$ represents milligrams of vitamin B4, and $r_C$ represents milligrams of vitamin C.

## Step 2: List all the constraints
The constraints given are:
- $z$ has a muscle growth index of 1 and an energy stability index of 21.
- $r_2$ has a muscle growth index of 25 and an energy stability index of 15.
- $r_4$ has a muscle growth index of 10 and an energy stability index of 8.
- $r_C$ has a muscle growth index of 16 and an energy stability index of 17.
- $z + 25r_2 \geq 47$
- $10r_4 + 16r_C \geq 44$
- $z + 16r_C \geq 32$
- $z + 25r_2 + 16r_C \geq 38$
- $z + 25r_2 + 10r_4 + 16r_C \geq 38$
- $15r_2 + 8r_4 \geq 18$
- $21z + 8r_4 \geq 21$
- $8r_4 + 17r_C \geq 21$
- $21z + 15r_2 \geq 25$
- $21z + 15r_2 + 8r_4 + 17r_C \geq 25$
- $9r_2 - 6r_4 \geq 0$
- $10z - 3r_2 \geq 0$
- $z + 25r_2 \leq 165$
- $25r_2 + 10r_4 \leq 79$
- $z + 10r_4 \leq 224$
- $15r_2 + 8r_4 + 17r_C \leq 113$
- $21z + 15r_2 + 8r_4 \leq 126$

## 3: Convert the problem into Gurobi code
We will use Gurobi's Python API to model and solve this problem.

```python
import gurobi

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

    # Define the variables
    z = model.addVar(name="z", lb=0)  # milligrams of zinc
    r2 = model.addVar(name="r2", lb=0)  # milligrams of vitamin B2
    r4 = model.addVar(name="r4", lb=0)  # milligrams of vitamin B4
    rC = model.addVar(name="rC", lb=0)  # milligrams of vitamin C

    # Objective function
    model.setObjective(7 * z + 5 * r2 + 4 * r4 + 7 * rC, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(z + 25 * r2 >= 47)
    model.addConstr(10 * r4 + 16 * rC >= 44)
    model.addConstr(z + 16 * rC >= 32)
    model.addConstr(z + 25 * r2 + 16 * rC >= 38)
    model.addConstr(z + 25 * r2 + 10 * r4 + 16 * rC >= 38)
    model.addConstr(15 * r2 + 8 * r4 >= 18)
    model.addConstr(21 * z + 8 * r4 >= 21)
    model.addConstr(8 * r4 + 17 * rC >= 21)
    model.addConstr(21 * z + 15 * r2 >= 25)
    model.addConstr(21 * z + 15 * r2 + 8 * r4 + 17 * rC >= 25)
    model.addConstr(9 * r2 - 6 * r4 >= 0)
    model.addConstr(10 * z - 3 * r2 >= 0)
    model.addConstr(z + 25 * r2 <= 165)
    model.addConstr(25 * r2 + 10 * r4 <= 79)
    model.addConstr(z + 10 * r4 <= 224)
    model.addConstr(15 * r2 + 8 * r4 + 17 * rC <= 113)
    model.addConstr(21 * z + 15 * r2 + 8 * r4 <= 126)

    # Optimize the model
    model.optimize()

    # Print the results
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("z: ", z.varValue)
        print("r2: ", r2.varValue)
        print("r4: ", r4.varValue)
        print("rC: ", rC.varValue)
    else:
        print("The model is infeasible")

optimize_problem()
```