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 November 11th, 2018, 12:20 PM #1 Newbie   Joined: Oct 2018 From: Turkey Posts: 23 Thanks: 0 simple inequality problem x and y integer -5
November 11th, 2018, 12:47 PM   #2
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Quote:
 Originally Posted by ketanco x and y integer -5
We want to maximize x and minimize y, and this is:

$\displaystyle (x,y)=(3,-7)$

And so:

$\displaystyle 2x-3y=6+21=27$

 November 12th, 2018, 08:55 AM #3 Senior Member   Joined: Dec 2015 From: somewhere Posts: 600 Thanks: 88 Let $\displaystyle 2x-3y$ be a sum $\displaystyle 2x-3y=2x+(-3y)$ Maximize of $\displaystyle -3y$ means minimize of $\displaystyle 3y$ Last edited by idontknow; November 12th, 2018 at 09:11 AM.
November 12th, 2018, 10:54 AM   #4
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Quote:
 Originally Posted by ketanco x and y integer -5
When you deal with inequalities involving integers make them $\le$ rather than $<$.

$-\ 5 < x < 4 \text { and } x \in \mathbb Z \implies -\ 4 \le x \le 3 \implies -\ 8 \le 2x \le 6.$

$-\ 8 < y < 1 \text { and } y \in \mathbb Z \implies -\ 7 \le y \le 0 \implies 21 \ge -\ 3y \ge 0 \implies 0 \le -\ 3y \le 21.$

$\therefore -\ 8 + 0 \le 2x - 3y \le 6 + 21 \implies -\ 8 \le 2x - 3y \le 27.$

 November 12th, 2018, 12:03 PM #5 Senior Member   Joined: Dec 2015 From: somewhere Posts: 600 Thanks: 88 What about maximize $\displaystyle \frac{x}{y}$ ?

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