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.

Question

Quizplus · Accepted Answer

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 points (50, 0) and (0, 12.5) are found by setting Y and X to 0 in the respective equations, indicating they are corner points of the feasible region. The origin (0, 0) is also part of the feasible region since it satisfies all constraints. Therefore, there must be at least four corner points, including (50, 0) and (0, 12.5), when considering the intersection of the constraints and the axes.

A Linear Programming Problem Has Two Constraints 2X + 4Y