Find the optimal solution for the following problem. $($Round your answers to $3$ decimal places.$)$

Minimize C $=11$x $+5$y

subject to $10$x $+12$y $>=19$

$13$x $+16$y $>=31$

and x $>=0,$ y $>=0.$

What is the optimal value of x$?$

What is the optimal value of y$?$

What is the minimum value of the objective function?