## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The factory produces two types of ice cream: maple pecan and mint chocolate. Each type requires time on two machines: a mixing machine and a freezing machine. The goal is to maximize profit given the constraints on machine availability.

Let's define the decision variables:
- \(x\): The number of batches of maple pecan ice cream.
- \(y\): The number of batches of mint chocolate ice cream.

The objective function to maximize profit is:
\[ \text{Maximize:} \quad 400x + 250y \]

The constraints based on machine availability are:
1. Mixing machine: \( 50x + 30y \leq 8000 \)
2. Freezing machine: \( 80x + 70y \leq 10000 \)

Additionally, \( x \geq 0 \) and \( y \geq 0 \) because the number of batches cannot be negative.

## Gurobi Code

```python
import gurobi

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

    # Define the decision variables
    x = model.addVar(name="maple_pecan_batches", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    y = model.addVar(name="mint_chocolate_batches", lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Objective function: Maximize profit
    model.setObjective(400 * x + 250 * y, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(50 * x + 30 * y <= 8000, name="mixing_machine_constraint")
    model.addConstr(80 * x + 70 * y <= 10000, name="freezing_machine_constraint")

    # Solve the model
    model.optimize()

    # Print the results
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution found. Production levels: {x.varValue} batches of maple pecan, {y.varValue} batches of mint chocolate.")
    else:
        print("No optimal solution found.")

solve_ice_cream_production()
```

However, to adhere strictly to the requirements and given that Gurobi's Python interface typically uses its own library `gurobipy`, let's correct and finalize the code:

```python
from gurobipy import *

def solve_ice_cream_production():
    # Create a new model
    model = Model()

    # Define the decision variables
    x = model.addVar(name="maple_pecan_batches", lb=0, vtype=GRB.CONTINUOUS)
    y = model.addVar(name="mint_chocolate_batches", lb=0, vtype=GRB.CONTINUOUS)

    # Objective function: Maximize profit
    model.setObjective(400 * x + 250 * y, GRB.MAXIMIZE)

    # Constraints
    model.addConstr(50 * x + 30 * y <= 8000, name="mixing_machine_constraint")
    model.addConstr(80 * x + 70 * y <= 10000, name="freezing_machine_constraint")

    # Solve the model
    model.optimize()

    # Print the results
    if model.status == GRB.OPTIMAL:
        print(f"Optimal solution found. Production levels: {x.varValue} batches of maple pecan, {y.varValue} batches of mint chocolate.")
    else:
        print("No optimal solution found.")

solve_ice_cream_production()
```