Using Binary Search to Sort a List in Python

My question accepts a (listof plane) structure where a plane is a list [airplane_code, date, price]:

• airplane_code is the plane name
• date is 1-365 inclusive where all dates might not be unique for each plane
• price is int[>=0] where all prices are unique for each plane

The function also produces a (listof plane). I need to filter this list according to the two other variable my function accepts (start_date and end_date) first and then by price (in ascending order). However I am restricted to using the binary search concept to sort for price:

def binary_search(lst, target):
    beginning = ...
    end = ...
    while ...:
        middle = ...
        if lst[middle] < target:
            ...
            ##update beginning and end
        else:
            ...
            ##update beginning and end

I cannot figure out how binary search would allow me to sort a list and would appreciate any help. This is what I have done until now (filtering for date variables given):

def determine(planes, start_date, end_date):
    correct_planes = []
    plane_price = []
    final_selection = []
    for plane in planes:
        if plane[1] >= start_date and plane[1] <= end_date:
            correct_planes.append(plane)
            plane_price.append(plane[2])

An example of how the function works:

plane_list = [['A11', 215, 300], ['A22', 260, 750], ['A33', 230, 600], ['A44', 300, 400]]

determine(plane_list, 200, 260) => [['A11', 215, 300], ['A33', 260, 600], ['A22', 260, 750]]