For-x-y-Z-such-that-7x-9y-405-Find-max-value-of-x-y-

Question Number 175799 by cortano1 last updated on 07/Sep/22

For x, y ε Z^{+} such that

7 x + 9 y = 405 . Find \max value

of x - y .

Answered by mr W last updated on 07/Sep/22

7 x + 9 y = 405

\Rightarrow x = 9 k + 54 > 0 \Rightarrow k ⩾ - 5

\Rightarrow y = - 7 k + 3 > 0 \Rightarrow k ⩽ 0

s = x - y = 9 k + 54 + 7 k - 3 = 16 k + 51

s_{m i n} = - 16 \times 5 + 51 = - 29

s_{m a x} = 16 \times 0 + 51 = 51

Commented by cortano1 last updated on 07/Sep/22

nice

Answered by blackmamba last updated on 07/Sep/22

l e t h = x - y a n d x = h + y

g i v e n c o n d i t i o n 7 x + 9 y = 405

\Rightarrow 7 (h + y) + 9 y = 405

\Rightarrow h = \frac{405 - 16 y}{7} = \frac{406 - 1 - 14 y - 2 y}{7}

\Rightarrow h = 58 - 2 y - \frac{2 y + 1}{7}

h m a x w h e n y m i n; y = 3

s o h_{m a x} = 58 - 6 - 1 = 51