## Step 1: Define the symbolic representation of the variables
The variables are 'milligrams of magnesium', 'milligrams of vitamin B1', and 'milligrams of vitamin K'. Let's denote them as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $3.78x_1 + 8.9x_2 + 5.8x_3$.

## Step 3: Define the constraints in symbolic notation
1. $13x_1 + 4x_2 + 6x_3 \geq 36$
2. $13x_1 + 4x_2 \geq 22$
3. $13x_1 + 4x_2 + 6x_3 \geq 53$
4. $6x_1 - 2x_2 \geq 0$
5. $3x_2 - 9x_3 \geq 0$
6. $13x_1 + 4x_2 \leq 89$

## 4: Consider the bounds of the variables and the immune support index
Each variable has an associated immune support index: $x_1$ has an index of 13, $x_2$ has an index of 4, and $x_3$ has an index of 6. The total immune support index for all variables combined has an upper bound of 162.

## 5: Formulate the problem in Gurobi
To formulate this problem in Gurobi, we need to define the model, add the variables, the objective function, and the constraints.

## 6: Write the Gurobi code
```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(lb=0, name="milligrams_of_magnesium", vtype=gurobi.GRB.CONTINUOUS)
x2 = model.addVar(lb=0, name="milligrams_of_vitamin_B1", vtype=gurobi.GRB.CONTINUOUS)
x3 = model.addVar(lb=0, name="milligrams_of_vitamin_K", vtype=gurobi.GRB.CONTINUOUS)

# Set the objective function
model.setObjective(3.78*x1 + 8.9*x2 + 5.8*x3, gurobi.GRB.MINIMIZE)

# Add constraints
model.addConstr(13*x1 + 4*x2 + 6*x3 >= 36, name="immune_support_index_1")
model.addConstr(13*x1 + 4*x2 >= 22, name="immune_support_index_2")
model.addConstr(13*x1 + 4*x2 + 6*x3 >= 53, name="immune_support_index_3")
model.addConstr(6*x1 - 2*x2 >= 0, name="constraint_4")
model.addConstr(3*x2 - 9*x3 >= 0, name="constraint_5")
model.addConstr(13*x1 + 4*x2 <= 89, name="constraint_6")

# Update the model
model.update()

# Solve the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objVal)
    print("Milligrams of magnesium: ", x1.varValue)
    print("Milligrams of vitamin B1: ", x2.varValue)
    print("Milligrams of vitamin K: ", x3.varValue)
else:
    print("The model is infeasible")
```

## 7: Symbolic Representation
```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 + 4*x2 + 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'
    ]
}
```