## Step 1: Define the symbolic representation of the variables
The variables are 'milligrams of potassium' and 'milligrams of calcium', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Convert the objective function into symbolic notation
The objective function to maximize is $4x_1 + 1x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
- Energy stability index for $x_1$: $13x_1$
- Digestive support index for $x_1$: $14x_1$
- Energy stability index for $x_2$: $10x_2$
- Digestive support index for $x_2$: $3x_2$
- Total combined energy stability index: $13x_1 + 10x_2 \geq 27$
- Total combined digestive support index: $14x_1 + 3x_2 \geq 10$
- Linear constraint: $-x_1 + 3x_2 \geq 0$
- Upper bound for total energy stability index: $13x_1 + 10x_2 \leq 61$
- Upper bound for total digestive support index: $14x_1 + 3x_2 \leq 37$

## 4: Consider the variable bounds and types
- $x_1$ is an integer
- $x_2$ can be a fraction

## 5: Formulate the problem in Gurobi
We will use Gurobi to solve this optimization problem.

## 6: Write down the problem in JSON format for clarity
```json
{
'sym_variables': [('x1', 'milligrams of potassium'), ('x2', 'milligrams of calcium')],
'objective_function': '4*x1 + 1*x2',
'constraints': [
    '13*x1 + 10*x2 >= 27',
    '14*x1 + 3*x2 >= 10',
    '-1*x1 + 3*x2 >= 0',
    '13*x1 + 10*x2 <= 61',
    '14*x1 + 3*x2 <= 37'
]
}
```

## 7: Implement the problem in Gurobi Python
```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="milligrams_of_potassium", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="milligrams_of_calcium")

    # Objective function
    model.setObjective(4 * x1 + x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(13 * x1 + 10 * x2 >= 27, name="energy_stability_index_min")
    model.addConstr(14 * x1 + 3 * x2 >= 10, name="digestive_support_index_min")
    model.addConstr(-x1 + 3 * x2 >= 0, name="linear_constraint")
    model.addConstr(13 * x1 + 10 * x2 <= 61, name="energy_stability_index_max")
    model.addConstr(14 * x1 + 3 * x2 <= 37, name="digestive_support_index_max")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of potassium: {x1.varValue}")
        print(f"Milligrams of calcium: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```