To solve this optimization problem using Gurobi, we first need to define the variables, the objective function, and the constraints as per the given problem description.

Let's denote:
- \(x_0\) as the milligrams of vitamin D,
- \(x_1\) as the milligrams of potassium,
- \(x_2\) as the milligrams of vitamin K.

The objective function to minimize is: \(8x_0 + 3x_1 + x_2\).

## Step 1: Define the Variables and Their Properties
We have three variables: \(x_0\), \(x_1\), and \(x_2\), representing milligrams of vitamin D, potassium, and vitamin K, respectively. \(x_0\) and \(x_2\) are required to be integers, while \(x_1\) can be a non-integer.

## 2: Formulate the Objective Function
The objective function is \(8x_0 + 3x_1 + x_2\).

## 3: Define the Constraints
The constraints are as follows:

1. Digestive support index for \(x_0\) is 3.
2. Cardiovascular support index for \(x_0\) is 3.
3. Cognitive performance index for \(x_0\) is 3.
4. Immune support index for \(x_0\) is 1.
5. Energy stability index for \(x_0\) is 1.

6. Digestive support index for \(x_1\) is 3.
7. Cardiovascular support index for \(x_1\) is 5.
8. Cognitive performance index for \(x_1\) is 2.
9. Immune support index for \(x_1\) is 1.
10. Energy stability index for \(x_1\) is 5.

11. Digestive support index for \(x_2\) is 1.
12. Cardiovascular support index for \(x_2\) is 5.
13. Cognitive performance index for \(x_2\) is 5.
14. Immune support index for \(x_2\) is 4.
15. Energy stability index for \(x_2\) is 2.

And the combined index constraints:
- \(3x_0 + 3x_1 \geq 2\)
- \(3x_1 + x_2 \geq 7\)
- \(3x_0 + 3x_1 + x_2 \geq 7\)
- \(5x_1 + 5x_2 \geq 6\)
- \(3x_0 + 5x_2 \geq 9\)
- \(3x_0 + 5x_1 + 5x_2 \geq 9\)
- \(3x_0 + 5x_2 \geq 3\)
- \(2x_1 + 5x_2 \geq 4\)
- \(3x_0 + 2x_1 + 5x_2 \geq 6\)
- \(3x_0 + 2x_1 + 5x_2 \geq 6\)
- \(x_1 + 4x_2 \geq 2\)
- \(x_0 + 4x_2 \geq 6\)
- \(x_0 + x_1 + 4x_2 \geq 5\)
- \(x_0 + x_1 + 4x_2 \geq 5\)
- \(5x_1 + 2x_2 \geq 4\)
- \(x_0 + 5x_1 \geq 2\)
- \(x_0 + x_1 + 2x_2 \geq 8\)
- \(x_0 + x_1 + 2x_2 \geq 8\)
- \(-7x_0 + 8x_1 \geq 0\)
- \(-7x_0 + 2x_2 \geq 0\)
- \(3x_0 + 2x_1 + 5x_2 \leq 14\)
- \(x_0 + x_1 + 4x_2 \leq 10\)
- \(x_0 + 2x_2 \leq 15\)
- \(5x_1 + 2x_2 \leq 13\)

## 4: Implement in Gurobi
```python
import gurobi

def optimize():
    model = gurobi.Model()
    
    # Define variables
    x0 = model.addVar(name="vitamin_D", vtype=gurobi.GRB.INTEGER)  # Milligrams of vitamin D
    x1 = model.addVar(name="potassium", vtype=gurobi.GRB.CONTINUOUS)  # Milligrams of potassium
    x2 = model.addVar(name="vitamin_K", vtype=gurobi.GRB.INTEGER)  # Milligrams of vitamin K

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

    # Constraints
    model.addConstr(3 * x0 <= 22, name="r0_constraint")
    model.addConstr(3 * x0 <= 50, name="r1_constraint")
    model.addConstr(3 * x0 <= 18, name="r2_constraint")
    model.addConstr(x0 <= 19, name="r3_constraint")
    model.addConstr(x0 <= 25, name="r4_constraint")

    model.addConstr(3 * x1 <= 22, name="r0_constraint_x1")
    model.addConstr(5 * x1 <= 50, name="r1_constraint_x1")
    model.addConstr(2 * x1 <= 18, name="r2_constraint_x1")
    model.addConstr(x1 <= 19, name="r3_constraint_x1")
    model.addConstr(5 * x1 <= 25, name="r4_constraint_x1")

    model.addConstr(x2 <= 22, name="r0_constraint_x2")
    model.addConstr(5 * x2 <= 50, name="r1_constraint_x2")
    model.addConstr(5 * x2 <= 18, name="r2_constraint_x2")
    model.addConstr(4 * x2 <= 19, name="r3_constraint_x2")
    model.addConstr(2 * x2 <= 25, name="r4_constraint_x2")

    model.addConstr(3 * x0 + 3 * x1 >= 2, name="combined_digestive_support")
    model.addConstr(3 * x1 + x2 >= 7, name="combined_digestive_support_2")
    model.addConstr(3 * x0 + 3 * x1 + x2 >= 7, name="combined_digestive_support_3")

    model.addConstr(5 * x1 + 5 * x2 >= 6, name="combined_cardiovascular_support_2")
    model.addConstr(3 * x0 + 5 * x2 >= 9, name="combined_cardiovascular_support_3")
    model.addConstr(3 * x0 + 5 * x1 + 5 * x2 >= 9, name="combined_cardiovascular_support_4")

    model.addConstr(3 * x0 + 5 * x2 >= 3, name="combined_cognitive_performance_2")
    model.addConstr(2 * x1 + 5 * x2 >= 4, name="combined_cognitive_performance_3")
    model.addConstr(3 * x0 + 2 * x1 + 5 * x2 >= 6, name="combined_cognitive_performance_4")

    model.addConstr(x1 + 4 * x2 >= 2, name="combined_immune_support_2")
    model.addConstr(x0 + 4 * x2 >= 6, name="combined_immune_support_3")
    model.addConstr(x0 + x1 + 4 * x2 >= 5, name="combined_immune_support_4")

    model.addConstr(5 * x1 + 2 * x2 >= 4, name="combined_energy_stability_2")
    model.addConstr(x0 + 5 * x1 >= 2, name="combined_energy_stability_3")
    model.addConstr(x0 + x1 + 2 * x2 >= 8, name="combined_energy_stability_4")

    model.addConstr(-7 * x0 + 8 * x1 >= 0, name="linear_constraint_1")
    model.addConstr(-7 * x0 + 2 * x2 >= 0, name="linear_constraint_2")

    model.addConstr(3 * x0 + 2 * x1 + 5 * x2 <= 14, name="upper_bound_cognitive")
    model.addConstr(x0 + x1 + 4 * x2 <= 10, name="upper_bound_immune")
    model.addConstr(x0 + 2 * x2 <= 15, name="upper_bound_energy_1")
    model.addConstr(5 * x1 + 2 * x2 <= 13, name="upper_bound_energy_2")

    # Solve the model
    model.optimize()

    # Print the results
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Vitamin D: ", x0.varValue)
        print("Potassium: ", x1.varValue)
        print("Vitamin K: ", x2.varValue)
    else:
        print("No optimal solution found")

optimize()
```