To solve the optimization problem described, we will use the Gurobi Python interface. The goal is to minimize the objective function subject to several constraints involving milligrams of magnesium, vitamin B1, and vitamin K.

The objective function to be minimized is:
\[3.78 \times \text{milligrams of magnesium} + 8.9 \times \text{milligrams of vitamin B1} + 5.8 \times \text{milligrams of vitamin K}\]

Constraints are as follows:
1. The immune support index from each milligram of magnesium is 13.
2. The immune support index from each milligram of vitamin B1 is 4.
3. The immune support index from each milligram of vitamin K is 6.
4. Total combined immune support index from magnesium and vitamin K should be at least 36.
5. Total combined immune support index from magnesium and vitamin B1 must be at least 22.
6. Total combined immune support index from all three (magnesium, vitamin B1, vitamin K) must be at least 53.
7. \(6 \times \text{milligrams of magnesium} - 2 \times \text{milligrams of vitamin B1} \geq 0\).
8. \(3 \times \text{milligrams of vitamin B1} - 9 \times \text{milligrams of vitamin K} \geq 0\).
9. Total combined immune support index from magnesium and vitamin B1 should be at most 89.

Given the fractional nature allowed for all variables, we can directly model this problem without needing to consider integer constraints.

Here is how you could implement this in Gurobi using Python:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define variables
milligrams_magnesium = m.addVar(name='milligrams_of_magnesium', lb=0)
milligrams_vitamin_b1 = m.addVar(name='milligrams_of_vitamin_B1', lb=0)
milligrams_vitamin_k = m.addVar(name='milligrams_of_vitamin_K', lb=0)

# Define the objective function
m.setObjective(3.78 * milligrams_magnesium + 8.9 * milligrams_vitamin_b1 + 5.8 * milligrams_vitamin_k, GRB.MINIMIZE)

# Add constraints
m.addConstr(13 * milligrams_magnesium + 6 * milligrams_vitamin_k >= 36, name='constraint_4')
m.addConstr(13 * milligrams_magnesium + 4 * milligrams_vitamin_b1 >= 22, name='constraint_5')
m.addConstr(13 * milligrams_magnesium + 4 * milligrams_vitamin_b1 + 6 * milligrams_vitamin_k >= 53, name='constraint_6')
m.addConstr(13 * milligrams_magnesium + 4 * milligrams_vitamin_b1 <= 89, name='constraint_9')
m.addConstr(6 * milligrams_magnesium - 2 * milligrams_vitamin_b1 >= 0, name='constraint_7')
m.addConstr(3 * milligrams_vitamin_b1 - 9 * milligrams_vitamin_k >= 0, name='constraint_8')

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print('Optimal solution found:')
    print(f'Milligrams of Magnesium: {milligrams_magnesium.x}')
    print(f'Milligrams of Vitamin B1: {milligrams_vitamin_b1.x}')
    print(f'Milligrams of Vitamin K: {milligrams_vitamin_k.x}')
    print(f'Objective Function Value: {m.objVal}')
else:
    print('No optimal solution found')
```