Consider the following LP formulation:

Minimize $z=0\mathrm{.}3x_1+0\mathrm{.}9x_2$

Subject to

$x_1+x_{2}800$

$0\mathrm{.}21x_1-0\mathrm{.}30x_{2}0$

$0\mathrm{.}03x_1-0\mathrm{.}01x_{2}0$

$x_1,x_{2}0$

a$.$ Add the following constraint and change the objective to maximization:

$x_1+x_{2}1500$

Find the optimum solution using Graphical Solution Method.

b$.$ Find ALL the corner point solutions $($i$.$e$.,$ coordinates$)$ along with their corresponding $z$ values to confirm the optimum solution you determined in part a$?$