Answer: Option $(B)$ $50$
$x\geq 4$ and $y\geq 4$ , So we can take both $x =5$ & $y = 5$
$x+y \geq 10,$ Satisfied , $5+5 = 10$
$2x + 3y \geq 20$. Satisfied.
This is in fact the minimum value.
Other options:
$4,4 \implies x+y \geq 10$ constraint fail
$4,5 \implies x+y \geq 10$ fail
$6,4 \implies$ Sum $=52$ which is more than $50$ and hence cannot be answer.
$7,3 \implies 49+9 = 58$ which is again greater than $50$ and hence cannot be the answer.