Question $1$:

Use the two phase simplex method to identify an initial BFS$.$ Select the NBV with the most negative

reduced cost to enter the basis if there are multiple potential entering NBVs$.$

min:$3x_1+8x_2$

s$.$t$.$

$-x_1+x_{2}6(c1)$

$2x_1-x_2=4(c2)$

$x_1,x_{2}0$

$($a$)$ Convert to standard form and identify an initial basis in phase $1,$ adding artificial variables where

necessary.

$($b$)$ Complete phase one of the simplex method.