Date

Minw$=4y_1+8y_2+6y_3$

$s.t,$

$y_1+2y_2+y_{3}3$

$2y_1-y_2-y_{3}2$

$-y_1+y_2=1$

$y_1,y_{2}0,y_{3}is$ unrestricted

$($a$)$ Solve through simplex method.

$($b$)$ Convert the given LPP to dual.

$($c$)$ Solve the dual IPP through Big$-$M Method.

$($d$)$ Verify both simplex and big$-$m solutions.