## Symbolic Representation

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

Let's define the symbolic variables as follows:

- $x_1$ represents the number of batches of sausages.
- $x_2$ represents the number of batches of burger patties.

The objective is to maximize profit. The profit per batch of sausages is $200, and the profit per batch of burger patties is $250. Therefore, the objective function can be represented as:

Maximize: $200x_1 + 250x_2$

The constraints are as follows:

1. The meat-grinder runs for at most 3000 hours per year. To produce one batch of sausages requires 2 hours on the meat-grinder, and to produce one batch of burger patties requires 4 hours on the meat-grinder. Therefore, the first constraint is:

$2x_1 + 4x_2 \leq 3000$

2. The meat-packer runs for at most 3000 hours per year. To produce one batch of sausages requires 3 hours on the meat-packer, and to produce one batch of burger patties requires 1.5 hours on the meat-packer. Therefore, the second constraint is:

$3x_1 + 1.5x_2 \leq 3000$

Additionally, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of batches cannot be negative.

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'batches of sausages'), ('x2', 'batches of burger patties')],
    'objective_function': '200*x1 + 250*x2',
    'constraints': [
        '2*x1 + 4*x2 <= 3000',
        '3*x1 + 1.5*x2 <= 3000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Sausages_and_Burger_Patties")

# Define the variables
x1 = model.addVar(name="x1", lb=0, vtype=gp.GRB.CONTINUOUS)  # batches of sausages
x2 = model.addVar(name="x2", lb=0, vtype=gp.GRB.CONTINUOUS)  # batches of burger patties

# Define the objective function
model.setObjective(200 * x1 + 250 * x2, gp.GRB.MAXIMIZE)

# Add the constraints
model.addConstr(2 * x1 + 4 * x2 <= 3000, name="meat_grinder_constraint")
model.addConstr(3 * x1 + 1.5 * x2 <= 3000, name="meat_packer_constraint")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal batches of sausages: {x1.varValue}")
    print(f"Optimal batches of burger patties: {x2.varValue}")
    print(f"Maximal profit: {model.objVal}")
else:
    print("The model is infeasible.")
```