ask expertQuestion $3.(20$PTS$)$

This answer should fit on: $2$ page$($s$).$

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Suppose we redefine SEF to be an LP in the form:

$mamize,c^{TT}x\frac{+}{b}ar(z)$

subject $to$

$,Ax=b$

$,x0$

That is$,$ we enforce the use of constraints $x0,$ rather than $x0.$ For a given LP in this new SEF,

we also redefine the notion of canonical form for a basis $B$ accordingly.

$($a$)$ Using the fact that every LP can be equivalently written in SEF as originally defined in the

book, prove that every LP can be equivalently written in this newly defined SEF.

$($b$)$ Adjust the simplex algorithm $($Algorithm $2\mathrm{.}1)$ in the book, so that it works with LPs which are

given in this new SEF, and justify your adjustments. $($You are not allowed to call the original

algorithm as a subroutine.$)$