3
$\begingroup$

I'm going through a worked example on the Knapsack problem: enter image description here

My problem is that I don't understand quite follow the last bulletpoint. Where does the $x_4 = 4/5$ comes from? I know $x_4$ has to be a fraction of 1 (otherwise it breaks the inequality) but why specifically $4/5$? Any insight is highly appreciated.

$\endgroup$
3
$\begingroup$

The (non-negative) variables $x_1,x_2,x_3,x_4$ must satisfy the constraint $$ 2x_1+2x_2+4x_3+5x_4 \leq 8. $$ If $x_1=x_2=1$ then this simplifies to $$ 4x_3+5x_4 \leq 4, $$ which implies in particular that $x_3 \leq 1$ and $x_4 \leq 4/5$ (since $x_3,x_4 \geq 0$).

$\endgroup$
  • $\begingroup$ Ok that clears everything up, thank you $\endgroup$ – eyes enberg Apr 17 '15 at 23:00

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.