(1) Write the standard form of the following LPs and solve them using simplex algorithm and find out
if LP has a unique optimal solution, multiple optimal solution or LP is unbounded. Show all the steps
and write all the optimal solutions and optimal value if there is any.
(a)
max $z = x_1 + 3x_2$
s.t.
$x_1 - 2x_2 \le 0$
$-2x_1 + x_2 \le 4$
$5x_1 + 3x_2 \le 15$
$x_1, x_2 \ge 0$
(b)
max $z = 2x_1 + 2x_2$
s.t.
$x_1 + x_2 \le 6$
$2x_1 + x_2 \le 13$
$x_1, x_2 \ge 0$
(c)
max $z = x_1 + 3x_2$
s.t.
$x_1 - 2x_2 \le 4$
$-x_1 + x_2 \le 3$
$x_1, x_2 \ge 0$
