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 in the feasible region.
D) The feasible region is triangular in shape, bounded by (50, 0), (33.3333, 8.3333), and (100, 0).
E) The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized.

Question

Quizplus · Accepted Answer

To graph the feasible region, we first graph the lines 2X + 4Y = 100 and 1X + 8Y = 100. These intersect at (50, 6.25). 
The line 2X + 4Y = 100 goes through (50, 0) and (0, 25), so we shade the region above the line. 
The line 1X + 8Y = 100 goes through (0, 12.5) and (100, 0), so we shade the region below the line. 
The feasible region is the intersection of these shaded regions, which forms a triangle bounded by (50,0), (33.333, 8.333), and (0, 12.5). Thus, option D is true.

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