Question

1. Determine all postive numbers x and y satisfying 12 = xy while 2x + y is as small as possible.

Answer 1

(2,6), (3,4)

Explanation:

I am assuming you are looking for Integer solutions exclusively.

The product of x and y is 12, so x and y must be factors of 12. Factors of 12 include:

• 1 * 12
• 2 * 6
• 3 * 4

Next, we plug these values into 2x+y so that the total is the smallest. Because there is no specific value for each variable, each of the factors can be plugged into either x or y, however it would be better to make sure the smaller variable gets multiplied.

2(1) + 12 = 14

2(2) + 6 = 10

2(3) + 4 = 10