## Symbolic Representation

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

Let's denote:
- \(x_1\) as the number of large sandwiches
- \(x_2\) as the number of small sandwiches

The objective is to maximize profit. Given that the profit per large sandwich is $5 and per small sandwich is $3.50, the objective function can be written as:
\[ \text{Maximize:} \quad 5x_1 + 3.5x_2 \]

The constraints are:
1. Preparation time: \(4x_1 + 3x_2 \leq 1000\)
2. Toasting time: \(5x_1 + 4x_2 \leq 1200\)
3. Non-negativity: \(x_1 \geq 0, x_2 \geq 0\)

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'large sandwiches'), ('x2', 'small sandwiches')],
    'objective_function': '5*x1 + 3.5*x2',
    'constraints': [
        '4*x1 + 3*x2 <= 1000',
        '5*x1 + 4*x2 <= 1200',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define variables
x1 = model.addVar(name="large_sandwiches", lb=0, vtype=gp.GRB.CONTINUOUS)
x2 = model.addVar(name="small_sandwiches", lb=0, vtype=gp.GRB.CONTINUOUS)

# Objective function: Maximize 5*x1 + 3.5*x2
model.setObjective(5*x1 + 3.5*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(4*x1 + 3*x2 <= 1000, name="preparation_time")
model.addConstr(5*x1 + 4*x2 <= 1200, name="toasting_time")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: large sandwiches = {x1.varValue}, small sandwiches = {x2.varValue}")
    print(f"Maximal profit: ${model.objVal:.2f}")
else:
    print("The model is infeasible.")
```