A linear programming problem has two constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100, plus nonnegativity constraints on X and Y. Which of the following statements about its feasible region is true?

A) There are four corner points including (50, 0) and (0, 12.5) .
B) The two corner points are (0, 0) and (50, 12.5) .
C) The graphical origin (0, 0) is not in the feasible region.
D) The feasible region includes all points that satisfy one constraint, the other, or both.
E) The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized.

The feasible region of a linear programming problem is defined by the intersection of all constraints, including nonnegativity constraints. The constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100, along with X ≥ 0 and Y ≥ 0, form a polygon on the coordinate plane. The corner points of this polygon can be found by solving the system of equations formed by the intersection of these lines, including the axes. (50, 0) and (0, 12.5) are points where each constraint intersects an axis, indicating they are corner points of the feasible region. There are typically four corner points in such a bounded region: where each constraint intersects the axes and where the constraints intersect each other, plus the origin if it's included within the constraints, which it is in this case since both X and Y can be 0 and still satisfy all constraints.