Question

methods for determining the vertices of the feasible region.

Answer 1

x > 0 and y >0 means the first quadrant

x+y >= 10 is the semiplane whose limit is the straight line

x+y = 10 => y = -x + 10. The angle between this line and the x axis is -45o and it past through the point (0,10)

To find which of the two semiplanes you need, think of a point. For instance, (0,0). 0+0 is ot >=10, then you need the semiplane that is above the line