Consider the following LP and its optimal tabeau:

$($a$)$ The dual optimal solution is $y_1=$

$,y_2=$

$($b$)$ the range of values of the right hand side $b_1$ of the first constraint for which the current

basis remains optimal is from

to

$($c$)$ the range of values of the right hand side $b_2$ of the second constraint for which the current

basis remains optimal is from

to

$($d$)$ if the right hand side of the first constraint is changed to $b_1=3,$ the new optimal solution

will be $x_1=$

$,x_2=$

$,x_3=$

$($e$)$ if the right hand side of the second constraint is changed to $b_2=5,$ the new optimal solution

will be $x_1=$

$,x_2=$

$,x_3=$