Minimize z $=$x$1+3$x$2-$x$3$

Subject to:

x$1+$x$2+$x$33$

$-$x$1+2$x$22$

$-$x$1+3$x$2+1$x$34$

Using the dual$-$simplex method, find the optimal solution to the primal problem.

$($f$)$What are the allowable decrease and allowable increase in the RHS value of the first

constraint of the primal problem to keep the current basis unchanged?

$($g$)$What is the cost of one unit increase in the RHS value of the first constraint of the primal

problem?

$($h$)$Suppose that we want to decrease the objective function value $($cost$)$of the first decision

variable. In what values can you decrease this cost so that the optimal solution of the

primal problem remains optimal?