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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<x<4 8<y<1 what is the maximum value of 2x3y? when i multiply first eqn by 2 and second by 3 and the add them up i get 13<2x3y<32 which makes the answer 31 but that is not even given in answer choices and the answer they say should be 27 . please help 
November 11th, 2018, 12:47 PM  #2  
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Quote:
$\displaystyle (x,y)=(3,7)$ And so: $\displaystyle 2x3y=6+21=27$  
November 12th, 2018, 08:55 AM  #3 
Senior Member Joined: Dec 2015 From: iPhone Posts: 482 Thanks: 73 
Let $\displaystyle 2x3y$ be a sum $\displaystyle 2x3y=2x+(3y)$ 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  
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  Quote:
$\ 5 < x < 4 \text { and } x \in \mathbb Z \implies \ 4 \le x \le 3 \implies \ 8 \le 2x \le 6.$ $\ 8 < y < 1 \text { and } y \in \mathbb Z \implies \ 7 \le y \le 0 \implies 21 \ge \ 3y \ge 0 \implies 0 \le \ 3y \le 21.$ $\therefore \ 8 + 0 \le 2x  3y \le 6 + 21 \implies \ 8 \le 2x  3y \le 27.$  
November 12th, 2018, 12:03 PM  #5 
Senior Member Joined: Dec 2015 From: iPhone Posts: 482 Thanks: 73 
What about maximize $\displaystyle \frac{x}{y}$ ?


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inequality, problem, simple 
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