What is the smallest possible product you can form from two non-negative numbers whose sum is 14? The minimum product is

Question

What is the smallest possible product you can form from two non-negative numbers whose sum is 14? 

The minimum product is

Answer 1

Let x = the first number. To be non-negative, x ≥ 0.

Let y = the second number. To be non-negative, y ≥ 0.

We are given that x + y = 14. Thus y = 14 - x.

The product p = x * (14 - x).

When 0 < x < 14, p is positive.

When x = 0 or 14, p = 0, a minimum.

When x > 14, x is positive and 14 - x is negative, and so the product is negative.

As x →∞, p becomes larger and more negative without bound. Hence, there is no minimum.

Answer 2

Since the non- negative numbers include the rationals, no minimal product exists.

If only the integers are allowed the product is 13.