if 2x+3y = 2020? find maximum value 3x+2y for x and natural number


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Question Number 84188 by jagoll last updated on 10/Mar/20

$if 2 x + 3 y = 2020 ?$ $find maximum value 3 x + 2 y for x and natural$ $number$
Commented by jagoll last updated on 10/Mar/20

$this diopthantine equation ?$
Commented by jagoll last updated on 10/Mar/20

$yes . my answer is correct . but my way$ $is different with you way sir$
Commented by mr W last updated on 10/Mar/20

$x = - 3 k + 1007 ⩾ 1$ $y = 2 k + 2 ⩾ 1$ $\Rightarrow 0 ⩽ k ⩽ 335$ $3 x + 2 y = 3 (- 3 k + 1007) + 2 (2 k + 2)$ $= 3025 - 5 k ⩽ 3025$ $= 3025 - 5 k ⩾ 1350$ $i . e . m a x i m u m o f 3 x + 2 y i s 3025 .$ $i . e . m i n i m u m o f 3 x + 2 y i s 1350 .$
Commented by mr W last updated on 11/Mar/20

$y e s . t h e r e a r e m a n y w a y s t o s o l v e .$ $i n o t o n l y w a n t e d t o k n o w t h e$ $m i n i m u m a n d m a x i m u m, b u t a l s o$ $w a n t e d t o k n o w t h e g e n e r a l s o l u t i o n$ $o f t h e e q u a t i o n a n d h o w m a n y s o l u t i o n s$ $i t h a s . t h e r e f o r e i s e l e c t e d t h i s w a y .$
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