if-2x-3y-2020-find-maximum-value-3x-2y-for-x-and-natural-number-

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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