Decision 1: Linear Programming "At least twice as many" meaning

Let x be the number of desk top diaries bought.

Let y be the number of pocket diaries bough.

There will need to be at least twice as many pocket diaries as desk top diaries.

Now why is the inequality 2x<_ y

Let x be the number of desk top diaries bought.

Let y be the number of pocket diaries bough.

There will need to be at least twice as many pocket diaries as desk top diaries.

Now why is the inequality 2x<_ y

If there is twice as many y as x then y=2x. "At least twice as many" means y could be 3x, 10x, pix, anything greater than or equal to 2x. Therefore y >= 2x.

This was a concept I struggled with when I first learned linear programming. If there's twice as many pocket as desktop, 2x=y. Then you just add the inequality bit. It might make it easier to use like 1/2y = x as that helps you visualise it better as you have half as many pocket diaries as desktop.

I'm not sure I understand the question... The inequality is just a mathematical expression for what you've said before.

It is just how the inequality relates.

So if a question said that "at most three times as many of x of y" would it be x>= 3y or 3y<= x

Note that as you've written it, you've got the same inequality twice. Let's say you want to write "x is at most three times as much as y". If you're unsure which way the inequality goes, plug in a value. For example:

y=1: Then 3y =3, and x can be anything up to 3 but no more, i.e. $x\leq 3y$.

(As a general rule, if you're having problem with notation or a basic concept or something, I would just plug in values or try really basic examples until I've got the hang of what we're trying to do. Especially helpful with anything to do with inequalities!)