Which of these sets of points are the corner points...pick a,b,c, or d?

Question

Which of these sets of points are the corner points for the feasible region satisfying the system of linear inequalities 2x + 8y < or = 32, 5x + 2y > or = 30, x> or =0, y > or =0?

a) (5,9), (4,0), (1/2, 4/9)
b) (0,4), (15, 0), (0, 0)
c) (0,4), (0,15), (4, 0), (4, 9)
d) (0, 4), (0, 15), (44/9, 25/9)

Answer 1

Are you sure the inequalities aren't 2x+8y >= 32 and 5x+2y<=30? This would lead to answer d. But they problem you stated (2x+8y <= 32 and 5x+2y>=30) leads to another answer not listed: (6,0), (16,0), and (44/9, 25/9).

Assuming the inequalities are 2x+8y >= 32 and 5x+2y<=30 we can show that:

y>= 4-x/4 and y<=15-5x/2

So at x = 0, y must be between 4 and 15.

Setting the two equations equal yields a third corner point:
4-x/4 = 15-5x/2

which is true at x=44/9. Plugging this x value into either equation above yields y = 25/9.

Answer 2

Go with R. J.