Consider the problem

maximize c$1$x$1+$ c$2$x$2$

s$.$t$.$ x$1+$ x$2<=1$

x$1,$ x$2>=0$

$.$

where c$1$ and c$2$ are constants such that c$1>$ c$2>=0.$ This is a linear programming problem. Assuming that the problem has an optimal feasible solution, use the FD$-$FONC to show that the unique optimal feasible solution x$$ is $(1,0)>$