To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's define:

- $x_1$ as the number of burritos made,
- $x_2$ as the number of sandwiches made.

The objective function is to maximize profit. Each burrito is sold for a profit of $2.5, and each sandwich is sold for a profit of $7. Therefore, the objective function can be written as:

Maximize: $2.5x_1 + 7x_2$

The constraints based on the given problem are:
1. The total amount of pork meat used does not exceed 5000 grams. Since each burrito requires 25 grams and each sandwich requires 15 grams, we have:
\[25x_1 + 15x_2 \leq 5000\]

2. At least four times the number of sandwiches are needed than burritos:
\[x_2 \geq 4x_1\]

3. There needs to be at least 6 burritos made:
\[x_1 \geq 6\]

4. Non-negativity constraints, as we cannot make a negative number of burritos or sandwiches:
\[x_1 \geq 0, x_2 \geq 0\]

Given this symbolic representation, the problem in JSON format is:

```json
{
    'sym_variables': [('x1', 'number of burritos'), ('x2', 'number of sandwiches')],
    'objective_function': '2.5*x1 + 7*x2',
    'constraints': ['25*x1 + 15*x2 <= 5000', 'x2 >= 4*x1', 'x1 >= 6', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's write the Gurobi code to solve this optimization problem:

```python
from gurobipy import *

# Create a new model
model = Model("Optimization_Problem")

# Define variables
x1 = model.addVar(vtype=GRB.CONTINUOUS, name="burritos", lb=0)
x2 = model.addVar(vtype=GRB.CONTINUOUS, name="sandwiches", lb=0)

# Set the objective function
model.setObjective(2.5*x1 + 7*x2, GRB.MAXIMIZE)

# Add constraints
model.addConstr(25*x1 + 15*x2 <= 5000, "pork_meat_limit")
model.addConstr(x2 >= 4*x1, "sandwich_burrito_ratio")
model.addConstr(x1 >= 6, "minimum_burritos")

# Optimize the model
model.optimize()

# Print results
if model.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Burritos: {x1.x}")
    print(f"Sandwiches: {x2.x}")
    print(f"Maximum Profit: ${model.objVal:.2f}")
else:
    print("No optimal solution found")
```