## Problem Description and Formulation

The ice cream shop's problem can be formulated as a linear programming optimization problem. The goal is to maximize profit by determining the number of regular (`x1`) and premium (`x2`) ice creams to produce, given certain constraints.

- The profit for each regular ice cream is $1.
- The profit for each premium ice cream is $2.50.
- The demand for regular ice cream is at most 40.
- The demand for premium ice cream is at most 25.
- The total number of ice creams that can be made is 60.

## Mathematical Formulation

- **Objective Function:** Maximize profit `P = 1*x1 + 2.5*x2`.
- **Constraints:**
  1. `x1 <= 40` (demand constraint for regular ice cream).
  2. `x2 <= 25` (demand constraint for premium ice cream).
  3. `x1 + x2 <= 60` (total production constraint).
  4. `x1 >= 0` and `x2 >= 0` (non-negativity constraints, as the number of ice creams cannot be negative).

## Gurobi Code

To solve this problem using Gurobi in Python, we can use the following code:

```python
import gurobi

def solve_ice_cream_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    x1 = model.addVar(lb=0, name="regular_ice_cream")  # Number of regular ice creams
    x2 = model.addVar(lb=0, name="premium_ice_cream")  # Number of premium ice creams

    # Objective function: Maximize profit
    model.setObjective(1*x1 + 2.5*x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(x1 <= 40, name="regular_demand_constraint")
    model.addConstr(x2 <= 25, name="premium_demand_constraint")
    model.addConstr(x1 + x2 <= 60, name="total_production_constraint")

    # Optimize the model
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: x1 = {x1.varValue}, x2 = {x2.varValue}")
        print(f"Maximum profit: ${1*x1.varValue + 2.5*x2.varValue:.2f}")
    else:
        print("No optimal solution found.")

# Run the function
solve_ice_cream_problem()
```

This code defines the optimization problem using Gurobi's Python interface, solves it, and then prints out the optimal production levels for regular and premium ice creams, along with the maximum achievable profit.