---
id: 5900f42b1000cf542c50ff3d
title: 'Problem 190: Maximising a weighted product'
challengeType: 5
forumTopicId: 301828
dashedName: problem-190-maximising-a-weighted-product
---

# --description--

Let $S_m = (x_1, x_2, \ldots, x_m)$ be the $m$-tuple of positive real numbers with $x_1 + x_2 + \cdots + x_m = m$ for which $P_m = x_1 \times {x_2}^2 \times \cdots \times {x_m}^m$ is maximised.

For example, it can be verified that $[P_{10}] = 4112$ ([ ] is the integer part function).

Find $\sum {[P_m]}$ for $2 ≤ m ≤ 15$.

# --hints--

`maximisingWeightedProduct()` should return `371048281`.

```js
assert.strictEqual(maximisingWeightedProduct(), 371048281);
```

# --seed--

## --seed-contents--

```js
function maximisingWeightedProduct() {

  return true;
}

maximisingWeightedProduct();
```

# --solutions--

```js
// solution required
```