To solve the optimization problem described, we first need to establish a symbolic representation of the variables and the constraints involved.

Let's denote:
- $x_1$ as the milligrams of magnesium,
- $x_2$ as the milligrams of vitamin B1,
- $x_3$ as the milligrams of vitamin K.

The objective function to minimize is given by:
\[3.78x_1 + 8.9x_2 + 5.8x_3\]

The constraints are as follows:
1. The total combined immune support index from milligrams of magnesium and milligrams of vitamin K should be no less than 36: 
\[13x_1 + 6x_3 \geq 36\]
2. The total combined immune support index from milligrams of magnesium and milligrams of vitamin B1 must be at least 22:
\[13x_1 + 4x_2 \geq 22\]
3. The total combined immune support index from all three (milligrams of magnesium, milligrams of vitamin B1, and milligrams of vitamin K) has to be as much or more than 53:
\[13x_1 + 4x_2 + 6x_3 \geq 53\]
4. This constraint is the same as the third one, so we will not repeat it.
5. Six times the number of milligrams of magnesium, plus -2 times the number of milligrams of vitamin B1 should be at minimum zero:
\[6x_1 - 2x_2 \geq 0\]
6. Three times the number of milligrams of vitamin B1, plus -9 times the number of milligrams of vitamin K should be greater than or equal to zero:
\[3x_2 - 9x_3 \geq 0\]
7. The total combined immune support index from milligrams of magnesium plus milligrams of vitamin B1 has to be equal to or less than 89:
\[13x_1 + 4x_2 \leq 89\]

Given these constraints and the objective function, we can represent our problem symbolically as follows:

```json
{
    'sym_variables': [('x1', 'milligrams of magnesium'), ('x2', 'milligrams of vitamin B1'), ('x3', 'milligrams of vitamin K')],
    'objective_function': '3.78*x1 + 8.9*x2 + 5.8*x3',
    'constraints': [
        '13*x1 + 6*x3 >= 36',
        '13*x1 + 4*x2 >= 22',
        '13*x1 + 4*x2 + 6*x3 >= 53',
        '6*x1 - 2*x2 >= 0',
        '3*x2 - 9*x3 >= 0',
        '13*x1 + 4*x2 <= 89'
    ]
}
```

To solve this optimization problem using Gurobi, we can use the following Python code:

```python
from gurobipy import *

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

# Define the variables
x1 = m.addVar(lb=0, name="milligrams_of_magnesium")
x2 = m.addVar(lb=0, name="milligrams_of_vitamin_B1")
x3 = m.addVar(lb=0, name="milligrams_of_vitamin_K")

# Define the objective function
m.setObjective(3.78*x1 + 8.9*x2 + 5.8*x3, GRB.MINIMIZE)

# Add constraints
m.addConstr(13*x1 + 6*x3 >= 36, name="constraint_1")
m.addConstr(13*x1 + 4*x2 >= 22, name="constraint_2")
m.addConstr(13*x1 + 4*x2 + 6*x3 >= 53, name="constraint_3")
m.addConstr(6*x1 - 2*x2 >= 0, name="constraint_4")
m.addConstr(3*x2 - 9*x3 >= 0, name="constraint_5")
m.addConstr(13*x1 + 4*x2 <= 89, name="constraint_6")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Milligrams of magnesium: {x1.x}")
    print(f"Milligrams of vitamin B1: {x2.x}")
    print(f"Milligrams of vitamin K: {x3.x}")
else:
    print("No optimal solution found")
```