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Both $x$ and $y$ are positive real numbers, and the point $(x,y)$ lies on or above both of the lines having equations $2x+5y = 10$ and $3x+4y = 12$. What is the least possible value of $8x+13y$?

 Mar 19, 2020
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With the info, we try to sum the equation to something useful. We turn the lines into inequalities. Adding the first inequality to two times the second gets us
 

\(8x+13y=(2x+5y)+2(3x+4y)\geq 10+2\cdot 12 = \boxed{34} \)

credit to aops for the solution

 

smileysmileysmiley

 Apr 6, 2020

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