$1[400]$

$[$a$][300]$ Solve the following linear program $($LP$)$ graphically $($Be sure to implement a reasonable scale $-$ that provides a READABLE GRAPH$).$ Identify the feasible region and the optimal solution. Plot the OPTIMAL objective function as a double dashed line broken line $)====($ through the optimal point and identify the optimal point. Label the feasible extreme points starting with $[x_1,x_2]=[0,0]$ as $A,$ and continuing counter$-$clockwise for the other feasible extreme points.

Plot the objective function for $Z=30$ as a dashed line broken line $(---------)$

Maximize $Z=5\mathrm{.}0x_1+6\mathrm{.}0x_2$

Subject to:

$x_{2}8$

$-4x_1+3x_{2}12$

$-1x_1+5x_{2}0$

$3x_1+4x_{2}50$

$1x_1+0x_{2}10$

$x_1,x_{2}0$

$[$b$][100]$ For each FEASIBLE Extreme Point in Problem $[$a$],$ complete the following table $($add additional rows as necessary$)$:

$\backslash$table$[[$Point$,,x2,Z,$lal? $[$Y$/$N$],$Why?$],[,,,,,]]$