For the LPP, Min $Z=5x+7y$ subject to $x≥0, y ≥0; 2x + y ≥ 8, x+2y ≥ 10, $ the basic feasible solutions are :

(10, 0), (2, 4) and (0, 8)

The correct answer is Option (2) → (10, 0), (2, 4) and (0, 8)

$x,y ≥0, 2x + y ≥ 8, x+2y ≥ 10$

finding intersection point

$2x+y=8$   ...(1)

$x+2y=10$  ...(2)

eq. (1) + eq. (2) 

$⇒3(x+y)=18$

so $x+y=6$  ...(3)

eq. (2) - eq. (1)

$⇒y-x=2$  ...(4)

eq. (3) + eq. (4)

$⇒2y=8⇒y=4$

from (3) $x=2$

so feasible points → (0, 8), (2, 4), (10, 0)