Max $3$X$1+4$X$2$

s$.$t$.3$X$1+2$X$2<6(1)$

$5$X$1+10$X$2<20(2)$

$2$X$1>1(3)$

X$1,$ X$2>0$

a$.$ Please use the graphical method to find the FEASIBLE REGION. Please list all the points used to draw the boundary straight lines and label the $3$ constraints in your graph.

b$.$ Please draw an objective function line in the graph of a$.$ and mark the optimal solution as a star. $($must list the equation and the points used to draw the line$)$

c$.$ Please get the optimal solution $($Must list the system of two equations, which cross at the star$)$: How much is X$1$ and X$2?$ You need to indicate the maximized objective function output.