Problem $2$:

Consider the following minimization problem:

Min $TC=,4x_1+2x_2$

$s.t.12x_1+4x_{2}600$

$,2x_1+8x_{2}800$

$,x_1,x_{2}0$

$($a$)$ Graph the feasible region. Label your constraints.

$($b$)$ Are there any redundant constraints, and if so$,$ which one$/$s$?$

$($c$)$ Label the extreme points of the feasible region. At each extreme point you are to state whether

each $x_j$ and $s_i$ are zero or non$-$zero.

$($d$)$ State the optimal values of $x_1,x_2$ and TC$.$ Show the objective function on your graph of part $($a$).$

$($e$)$ Suppose the price of $x_2(P_2)$ increases to $4.$ What is the new optimal solution?

$($f$)$ Suppose the price of $x_2(P_2)$ increases to $18.$ What is the new optimal solution? State the values

of the $x_j$ and $s_i.$