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

Let's define the symbolic variables:
- $x_1$ = kilograms of enriched hay per cow per day
- $x_2$ = kilograms of chicken scraps per cow per day

The objective is to minimize the cost of feeding the cows, which can be represented as:
\[ \text{Minimize:} \quad 200x_1 + 350x_2 \]

The constraints based on the nutritional requirements are:
1. Protein: $0.3x_1 + 0.6x_2 \geq 1.5$
2. Vitamins: $0.1x_1 + 0.2x_2 \leq 0.5$
3. Minerals: $0.15x_1 + 0.05x_2 \geq 0.5$

Also, $x_1 \geq 0$ and $x_2 \geq 0$ since the amounts of feed cannot be negative.

## Step 2: Convert the problem into a Gurobi-compatible format

To scale up for 30 cows, we multiply the constraints by 30, but since we're optimizing per cow, we'll keep it as is for now and consider the entire problem for 30 cows in the Gurobi implementation.

## 3: Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'kilograms of enriched hay per cow per day'), ('x2', 'kilograms of chicken scraps per cow per day')],
    'objective_function': '200*x1 + 350*x2',
    'constraints': [
        '0.3*x1 + 0.6*x2 >= 1.5', 
        '0.1*x1 + 0.2*x2 <= 0.5', 
        '0.15*x1 + 0.05*x2 >= 0.5', 
        'x1 >= 0', 
        'x2 >= 0'
    ]
}
```

## 4: 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="enriched_hay", lb=0)
    x2 = model.addVar(name="chicken_scraps", lb=0)

    # Objective function: minimize cost
    model.setObjective(200 * x1 + 350 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(0.3 * x1 + 0.6 * x2 >= 1.5, name="protein_requirement")
    model.addConstr(0.1 * x1 + 0.2 * x2 <= 0.5, name="vitamin_limit")
    model.addConstr(0.15 * x1 + 0.05 * x2 >= 0.5, name="mineral_requirement")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Enriched Hay: {x1.varValue} kg/cow/day")
        print(f"Chicken Scraps: {x2.varValue} kg/cow/day")
        print(f"Total Cost: ${model.objVal:.2f}/cow/day")
        print(f"For 30 cows, total cost: ${model.objVal * 30:.2f}/day")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```