$[$a$][100]$ Provide the graphical solution of the following LP$.($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 $(=$ through the optimal point optimal point and identify the optimal point on the graph.

Maximize $Z=15x_1+15x_2$

s$.$ t$.$

$-1x_1+2x_{2}6(1)(Use$ Slack $x_3)$

$4x_1+3x_{2}24(2)(Use$ Slack $x_4)$

$5x_1.18(3)(Use$ Slack $x_5)$

$2x_1-1x_{2}4(4)(Use$ Slack $x_6)$

$1x_{2}4(5)(Use$ Slack $x_7)$

$x_1,x_{2}0$

Label the feasible extreme points starting with $[x_1,x_2]=[,]$ as $A,$ and continuing clockwise through $G.$