How can I push an element into array at a sorted index position?

Question

Say I have an array already with these articles, ordered by lowest to highest price:

[
  { title: "Article 3", price: 1.49 },
  { title: "Article 1", price: 3.00 },
  { title: "Article 4", price: 5.99 },
  { title: "Article 2", price: 19.99 }
]

Basically I would like to push another article into the array at the correct position (by price). How can I do so?

The new article I'm pushing may have the following properties:

{ title: "Article 5", price: 12.00 }

I'm expecting the article to appear at index 3 (between article 4 and 2).

UPDATE (SOLUTION)

I created a prototype method using @klutt's answer with binary search algorithm:

Array.prototype.pushSorted = function(el, compareFn) {
  this.splice((function(arr) {
    var m = 0;
    var n = arr.length - 1;

    while(m <= n) {
      var k = (n + m) >> 1;
      var cmp = compareFn(el, arr[k]);

      if(cmp > 0) m = k + 1;
        else if(cmp < 0) n = k - 1;
        else return k;
    }

    return -m - 1;
  })(this), 0, el);

  return this.length;
};

const sortByPrice = (a, b) => a.price > b.price;
theArray.pushSorted({ title: "Article 5", price: 12.00 }, sortByPrice);

Answer 1

The Update (Solution) still doesn't work great. Items that should go either to the start or end get placed in the wrong position, see this revised solution based on the same code:

Array.prototype.pushSorted = function(el, compareFn) {
  let index = (function(arr) {
    var m = 0;
    var n = arr.length - 1;

    while(m <= n) {
      var k = (n + m) >> 1;
      var cmp = compareFn(el, arr[k]);

      if(cmp > 0) m = k + 1;
        else if(cmp < 0) n = k - 1;
        else {
          console.log(`m=${m} k=${k}`)
          return k;
        };
    }


    return -m - 1;
  })(this);

  if (index >= 0)
    this.splice(index, 0, el);
  else if (index < 0)
    this.splice((index * -1) - 1, 0, el);

  return this.length;
};

Sample usage:

a = [1, 2, 3, 4, 5]
a.pushSorted(2.5, (a,b) => a - b);
a.pushSorted(8, (a,b) => a - b);
a.pushSorted(0.5, (a,b) => a - b);