To solve the optimization problem described, we first need to convert the natural language description into a symbolic representation. This involves defining variables for the quantities of subs and flatbreads to be made, formulating the objective function based on profit per item, and translating the time constraints into algebraic expressions.

Let's denote:
- \(x_1\) as the number of subs to be made.
- \(x_2\) as the number of flatbreads to be made.

The symbolic representation is thus:
```json
{
  'sym_variables': [('x1', 'number of subs'), ('x2', 'number of flatbreads')],
  'objective_function': '3*x1 + 2.50*x2',
  'constraints': ['3*x1 + 4*x2 <= 2000', '2*x1 + x2 <= 2200', 'x1 >= 0', 'x2 >= 0']
}
```

The reasoning behind this representation is as follows:
- The objective function `3*x1 + 2.50*x2` aims to maximize profit, where $3 is the profit per sub and $2.50 is the profit per flatbread.
- The constraints are:
  - `3*x1 + 4*x2 <= 2000`: This represents the total preparation time constraint. Each sub takes 3 minutes of preparation, and each flatbread takes 4 minutes.
  - `2*x1 + x2 <= 2200`: This represents the total toasting time constraint. Each sub takes 2 minutes of toasting, and each flatbread takes 1 minute.
  - `x1 >= 0` and `x2 >= 0`: These constraints ensure that the number of subs and flatbreads made cannot be negative.

Now, let's write the Gurobi code in Python to solve this linear programming problem:

```python
from gurobipy import *

# Create a new model
m = Model("Sandwich_Store")

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="subs")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="flatbreads")

# Set the objective function
m.setObjective(3*x1 + 2.50*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(3*x1 + 4*x2 <= 2000, "preparation_time")
m.addConstr(2*x1 + x2 <= 2200, "toasting_time")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of subs: {x1.x}")
    print(f"Number of flatbreads: {x2.x}")
    print(f"Maximum profit: ${3*x1.x + 2.50*x2.x:.2f}")
else:
    print("No optimal solution found")
```