Question $1$:

Solve the following problem using simplex method. Let $\{s_1,s_2,s_3\}$ be your initial basis. Select the NBV with the most negative reduced cost to enter the basis if there are multiple potential entering NBVs$.$

max:$3x_1+8x_2$

s$.$t$.$

$-x_1+x_{2}6$

$2x_1+3x_{2}21$

$2x_1-x_{2}4$

$x_1,x_{2}0$