## Step 1: Define the symbolic representation of the problem

Let's define the symbolic variables:
- $x_1$ represents the number of servings of noodles
- $x_2$ represents the number of servings of cakes

The objective is to minimize the cost, where noodles cost $3 per serving and cakes cost $5 per serving. So, the objective function is $3x_1 + 5x_2$.

## Step 2: Define the constraints

The constraints based on the problem description are:
- The total proteins from noodles and cakes should be at most 100 units: $5x_1 + 4x_2 \leq 100$
- The total minerals from noodles and cakes should be at most 30 units: $12x_1 + 8x_2 \leq 30$
- The number of servings of noodles and cakes cannot be negative: $x_1 \geq 0, x_2 \geq 0$

## 3: Symbolic representation in JSON format

```json
{
    'sym_variables': [('x1', 'servings of noodles'), ('x2', 'servings of cakes')],
    'objective_function': '3*x1 + 5*x2',
    'constraints': [
        '5*x1 + 4*x2 <= 100',
        '12*x1 + 8*x2 <= 30',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## 4: Convert the problem into Gurobi code

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(lb=0, name="noodles")
    x2 = model.addVar(lb=0, name="cakes")

    # Define the objective function
    model.setObjective(3*x1 + 5*x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(5*x1 + 4*x2 <= 100, name="protein_constraint")
    model.addConstr(12*x1 + 8*x2 <= 30, name="mineral_constraint")

    # Optimize the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Servings of noodles: {x1.varValue}")
        print(f"Servings of cakes: {x2.varValue}")
        print(f"Total cost: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```