"""Create reasoning_engine
Generated by Phi-Octopus Eden
2025-11-07 04:47:21.728321
"""

```python
from typing import List, Dict

class ReasoningEngine:
    """
    A simple reasoning engine that solves a specific problem of determining 
    whether an item can be placed in a knapsack given its value and weight.
    
    The knapsack has a limited capacity, and the goal is to maximize the total
    value without exceeding this capacity. This example uses dynamic programming
    for a solution.
    """
    
    def __init__(self, max_weight: int):
        self.max_weight = max_weight

    def create_knapsack_table(self, values: List[int], weights: List[int]) -> Dict[int, (int, int)]:
        """
        Creates a table that keeps track of the maximum value and weight at each capacity up to `max_weight`.
        
        Args:
        - values: A list of integers representing the values of items.
        - weights: A list of integers representing the weights of items.
        
        Returns:
        A dictionary where keys are the capacities from 0 to max_weight, and values are tuples (value, weight) 
        representing the maximum value and weight achievable at each capacity.
        """
        n = len(values)
        table = {(i, j): (0, 0) for i in range(n + 1) for j in range(self.max_weight + 1)}
        
        for i in range(1, n + 1):
            for w in range(self.max_weight + 1):
                if weights[i - 1] <= w:
                    value_without_item = table[(i - 1, w)][0]
                    value_with_item = values[i - 1] + table[(i - 1, w - weights[i - 1])][0]
                    table[(i, w)] = (max(value_without_item, value_with_item), max(table[(i - 1, w)][1], 
                                                                                 values[i - 1] + table[(i - 1, w - weights[i - 1])][1]))
                else:
                    table[(i, w)] = table[(i - 1, w)]
        return table

    def get_max_value_and_weight(self) -> (int, int):
        """
        Returns the maximum value and weight that can be achieved within the knapsack's capacity.
        
        Returns:
        A tuple containing the maximum value and weight.
        """
        max_value, max_weight = self.create_knapsack_table([100, 200, 300], [50, 70, 80])[(len([100, 200, 300]), self.max_weight)]
        return max_value, max_weight


# Example Usage:
knapsack = ReasoningEngine(max_weight=160)
max_val, max_wt = knapsack.get_max_value_and_weight()
print(f"Maximum value: {max_val}, Maximum weight: {max_wt}")
```

This code demonstrates a simple reasoning engine that uses dynamic programming to solve the 0/1 Knapsack problem. The `create_knapsack_table` method constructs a table for optimization, and `get_max_value_and_weight` retrieves the optimized solution.