Solve the following LP problem using simplex method: To Maximize: $2$Y $+5$Y $+7$Z subject to$.3$X $+2$Y $+4$Z $=100$ X $+4$Y $+2$Z $=100$ X $+$Y $+3$Z $<==100$ X$,$ Y$,$ Z $>=0$

Divide by pivot column.

Solution mix X Y$2$ Z S$1$ S$2$ S$3$ RHS

$0$S$1324$

$100100100/4=25$

$0$s$2142010100100/2=50$

$0$s$3113001100100/3=33\mathrm{.}33$

P $257$

$0000$

Pivot number.

Highest positive value in the profit row indicates the pivot column $($Z$1$ will be part of the next solution mix$)$