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

Let's denote:
- $x_1$ as the number of tuna salad sandwiches
- $x_2$ as the number of chicken salad sandwiches

The objective is to minimize the cost, which can be represented as $5x_1 + 7x_2$.

The constraints are:
- Protein: $20x_1 + 25x_2 \geq 100$
- Fat: $25x_1 + 15x_2 \geq 150$
- Non-negativity: $x_1 \geq 0, x_2 \geq 0$

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

We will use the Gurobi library in Python to solve this linear programming problem.

## Step 3: Write down the symbolic representation in the required format

```json
{
    'sym_variables': [('x1', 'tuna salad sandwiches'), ('x2', 'chicken salad sandwiches')],
    'objective_function': '5*x1 + 7*x2',
    'constraints': [
        '20*x1 + 25*x2 >= 100',
        '25*x1 + 15*x2 >= 150',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Step 4: Implement the problem in Gurobi Python

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="tuna_salad_sandwiches", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(name="chicken_salad_sandwiches", lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Objective function: minimize 5*x1 + 7*x2
    model.setObjective(5 * x1 + 7 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(20 * x1 + 25 * x2 >= 100, name="protein_constraint")
    model.addConstr(25 * x1 + 15 * x2 >= 150, name="fat_constraint")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Tuna salad sandwiches: {x1.varValue}")
        print(f"Chicken salad sandwiches: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```