Graphically solve the following LPs in questions $2-5.$ Clearly show the isoprofit$/$isocost lines. Clearly

state which case applies $($unique optimal solution, multiple solutions, unbounded, infeasible$).$ If there are

multiple optimal solutions, please write down the set of optimal solutions. In each problem also solve the

problem in which $$max$"$ is replaced by $$min$".$

In the $$min$"$ case it may be possible to just give a quick logical argument to prove that it is the optimal

solution, rather than drawing the isocost lines. If this is the case, then provide that argument.

max

x

$4$x$1+$ x$2$

s$.$t$.8$x$1+2$x

x$1+2$x

$ma{x}_x,4x_1+x_2$

$s.t.8x_1+2x_{2}16$

$,x_1+2x_{2}10$

$,x_1,x_{2}0.$