Problem E : 6271

 Click on the image and use the password : ogeometrie . The QR code on page 2 contains a link to the Books in my Electronic Library. (Click on the year of publication. Same password if needed.) A collection of important magazines is at the letter G : GAZETA MATEMATICĂ seria B.

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                          " E : 6271*.  Find the maximum and minimum of the sum  $x+y$

                                                   and the product  $xy$ , knowing that  $5x+6y=150$ ,

 and  $x\; and\; y$  are natural numbers different from zero.           

{author : } Gh. MARGHESCU, student, București "

ANSWER CiP

$max\;(x+y)=29$  for  $x=24\;, \;y=5$

$min\;(x+y)=26$   for  $x=6\;,\;y=20$

$max\;(x\cdot y)=180$  for  $x=12\;,\;y=15\;\;or\;\;x=18\;,\;y=10$

$min\;(x\cdot y)=120$  for  $x=6\;,\;y=20\;\;or\;\;x=24\;,\;y=5$

Solution CiP

(to continue)