## Step 1: Define the symbolic representation of the problem
Let's denote the amount of regular supplementation as $x_1$ grams and the amount of premium supplementation as $x_2$ grams.

## Step 2: Convert the natural language description into a symbolic representation
The symbolic variables are:
- $x_1$ : regular supplementation
- $x_2$ : premium supplementation

## 3: Determine the objective function
The objective is to minimize the cost. The cost of regular supplementation is $0.04 per gram, and the cost of premium supplementation is $0.08 per gram. Therefore, the objective function is:
\[ \text{Minimize:} \quad 0.04x_1 + 0.08x_2 \]

## 4: Define the constraints
The constraints based on the requirements are:
- Iron requirement: $20\%$ of $x_1 + 25\%$ of $x_2 \geq 30$ grams
- Calcium requirement: $30\%$ of $x_1 + 40\%$ of $x_2 \geq 50$ grams
- Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## 5: Convert constraints into algebraic form
- Iron requirement: $0.20x_1 + 0.25x_2 \geq 30$
- Calcium requirement: $0.30x_1 + 0.40x_2 \geq 50$

## 6: Symbolic representation in JSON format
```json
{
'sym_variables': [('x1', 'regular supplementation'), ('x2', 'premium supplementation')],
'objective_function': '0.04x1 + 0.08x2',
'constraints': ['0.20x1 + 0.25x2 >= 30', '0.30x1 + 0.40x2 >= 50', 'x1 >= 0', 'x2 >= 0']
}
```

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

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

    # Define variables
    x1 = model.addVar(name="regular_supplementation", lb=0, ub=float('inf'))
    x2 = model.addVar(name="premium_supplementation", lb=0, ub=float('inf'))

    # Objective function: minimize 0.04x1 + 0.08x2
    model.setObjective(0.04 * x1 + 0.08 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(0.20 * x1 + 0.25 * x2 >= 30, name="iron_requirement")
    model.addConstr(0.30 * x1 + 0.40 * x2 >= 50, name="calcium_requirement")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Regular supplementation: {x1.varValue} grams")
        print(f"Premium supplementation: {x2.varValue} grams")
        print(f"Total cost: ${model.objVal:.2f}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```