$13$:$48$ @ $*$

$03\mathrm{.}01\mathrm{.}2024$

ENM$203$ Linear Programming Homework IV

Due: $5\mathrm{.}01\mathrm{.}202417$:$00$

ASSIGNMENT IV

ENM$203$ Linear Programming

Consider the following LP and its optimal tableau:

$\backslash$table$[[,,)],[,,.,.,-,$cdotscdots,..,,$-,],[2,x_1,x_2,,x_1,s_1,e_2,a_2,a_1,$rhs$],[1,1,0,,0,1,0,M,M+3,80],[0,-3,0,,0,1,1,-1,-2,15],[0,0,0,,1,1,0,0,-2,40],[0,1,1,,0,0,0,0,1,10]]$

a$.$ Find the dual of this LP and its optimal solution.

b$.$ Find the range of values of the objective function coefficient of $x_1$ for which the current basis remains optimal.

c$.$ Find the range of values of the objective function coef$-$ ficient for $x_2$ for which the current basis remains optimal.