## Step 1: Define the symbolic representation of the problem
The problem involves minimizing an objective function subject to several constraints. Let's define the symbolic variables:
- $x_1$ represents the milligrams of potassium
- $x_2$ represents the milligrams of vitamin D
- $x_3$ represents the milligrams of vitamin B1

The objective function to minimize is $5.1x_1 + 6.54x_2 + 7.3x_3$.

## Step 2: Translate the constraints into symbolic notation
The constraints given are:
1. The digestive support index from $x_1$ is $16x_1$.
2. The digestive support index from $x_2$ is $5x_2$.
3. The digestive support index from $x_3$ is $8x_3$.
4. The total combined digestive support index from $x_1$ and $x_2$ must be at least 20: $16x_1 + 5x_2 \geq 20$.
5. The total combined digestive support index from $x_1$, $x_2$, and $x_3$ must be at least 20: $16x_1 + 5x_2 + 8x_3 \geq 20$.
6. $2x_2 - 3x_3 \geq 0$.
7. $7x_1 - 5x_2 \geq 0$.

## 3: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [('x1', 'milligrams of potassium'), ('x2', 'milligrams of vitamin D'), ('x3', 'milligrams of vitamin B1')],
    'objective_function': '5.1*x1 + 6.54*x2 + 7.3*x3',
    'constraints': [
        '16*x1 + 5*x2 >= 20',
        '16*x1 + 5*x2 + 8*x3 >= 20',
        '2*x2 - 3*x3 >= 0',
        '7*x1 - 5*x2 >= 0'
    ]
}
```

## 4: Implement the optimization problem using Gurobi
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="x1", lb=0)  # milligrams of potassium
    x2 = model.addVar(name="x2", lb=0)  # milligrams of vitamin D
    x3 = model.addVar(name="x3", lb=0)  # milligrams of vitamin B1

    # Define the objective function
    model.setObjective(5.1 * x1 + 6.54 * x2 + 7.3 * x3, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(16 * x1 + 5 * x2 >= 20, name="constraint1")
    model.addConstr(16 * x1 + 5 * x2 + 8 * x3 >= 20, name="constraint2")
    model.addConstr(2 * x2 - 3 * x3 >= 0, name="constraint3")
    model.addConstr(7 * x1 - 5 * x2 >= 0, name="constraint4")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of potassium: {x1.varValue}")
        print(f"Milligrams of vitamin D: {x2.varValue}")
        print(f"Milligrams of vitamin B1: {x3.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```