Answer -> Option $B)$ $50$
$x>=4$ and $y>=4$ , So we can take both $x =5$ & $y = 5$
$x+y >= 10$ $=>$ Satisfied , $5+5 = 10$
$2x + 3y >= 20$. Satisfied.
This is infact minimum value.
Other options =>
$4,4 => x+y$ constraint fail
$4,5 => x+y$ fail
$6,4 =>$ Still giving $52$ as sum which is more than $50$ !, This can not be answer.
$7,3 => 49+9 > 58 > 50$.