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

Let's denote the number of vegetarian meals as $x_1$ and the number of meat meals as $x_2$. The objective is to minimize the total cost, which is $4x_1 + 6x_2$. The constraints are:

- Protein requirement: $10x_1 + 30x_2 \geq 100$
- Carb requirement: $20x_1 + 15x_2 \geq 150$
- Non-negativity: $x_1 \geq 0, x_2 \geq 0$

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

The symbolic representation can be translated into a Gurobi-compatible format as follows:

```json
{
    'sym_variables': [('x1', 'vegetarian meals'), ('x2', 'meat meals')],
    'objective_function': '4*x1 + 6*x2',
    'constraints': [
        '10*x1 + 30*x2 >= 100',
        '20*x1 + 15*x2 >= 150',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Step 3: Write the Gurobi code in Python

Now, let's write the Gurobi code in Python:

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="vegetarian_meals", lb=0, ub=gurobi.GRB.INFINITY)
    x2 = model.addVar(name="meat_meals", lb=0, ub=gurobi.GRB.INFINITY)

    # Define the objective function
    model.setObjective(4 * x1 + 6 * x2, gurobi.GRB.MINIMIZE)

    # Define the constraints
    model.addConstr(10 * x1 + 30 * x2 >= 100, name="protein_requirement")
    model.addConstr(20 * x1 + 15 * x2 >= 150, name="carb_requirement")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Vegetarian meals: {x1.varValue}")
        print(f"Meat meals: {x2.varValue}")
        print(f"Total cost: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```