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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 $\displaystyle \frac{x}{y}$ ? Tags inequality, problem, simple Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post ERohleder Elementary Math 2 July 2nd, 2016 01:43 PM david007killer Calculus 5 October 31st, 2015 05:08 PM MageKnight Number Theory 2 May 11th, 2014 09:10 PM Havoc Math Events 2 October 26th, 2010 08:15 AM forcesofodin Geometry 0 July 28th, 2010 02:43 PM

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