To solve this optimization problem, we first need to define the decision variables and the objective function. Let's denote the number of subs as `x` and the number of flatbreads as `y`. The profit per sub is $3, and the profit per flatbread is $2.50, so our objective function, which represents the total profit, can be written as `3x + 2.5y`.

The constraints are based on the preparation and toasting times for subs and flatbreads, along with the available time for these activities. Each sub takes 3 minutes of preparation and 2 minutes of toasting, while each flatbread takes 4 minutes of preparation and 1 minute of toasting. The store has 2000 minutes available for preparation and 2200 minutes for toasting. This gives us two constraints:

1. Preparation time constraint: `3x + 4y <= 2000`
2. Toasting time constraint: `2x + y <= 2200`

Additionally, since the number of subs and flatbreads cannot be negative, we have non-negativity constraints:
- `x >= 0`
- `y >= 0`

Now, let's formulate this problem in Gurobi using Python:

```python
from gurobipy import *

# Create a model
m = Model("Sandwich_Store_Optimization")

# Define the decision variables
x = m.addVar(vtype=GRB.CONTINUOUS, name="subs", lb=0)  # Number of subs
y = m.addVar(vtype=GRB.CONTINUOUS, name="flatbreads", lb=0)  # Number of flatbreads

# Define the objective function: Maximize profit
m.setObjective(3*x + 2.5*y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(3*x + 4*y <= 2000, name="preparation_time")  # Preparation time constraint
m.addConstr(2*x + y <= 2200, name="toasting_time")  # Toasting time constraint

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: {x.varName} = {x.x}, {y.varName} = {y.x}")
    print(f"Maximum profit: {m.objVal}")
else:
    print("No optimal solution found")
```