Show that when both systems are feasible, the optimum values for

$($

P

$)$

$$and

$($

D

$)$

$$are

the same.

Hint: Rewrite

$($

P

$)$

$$and

$($

D

$)$

$$as equivalent systems of the form max

$\{$tilde$($c

$)$

T

$($tilde$($x$))|($tilde$($A$))($tilde$($x$))$

$<=$

$($tilde$($b$))\}$

and min

$\{$tilde$($b

$)$

T

$($tilde$($y$))|$tilde$($y

$)$

T

$($tilde$($A$))$

$=$

tilde

$($c

$)$

T

$,$

$($tilde$($y$))$

$>=$

$0\}$

$$and use the result from the lecture.