The feasible region in the diagram below is consistent with which one of the following constraints?
A)8X1 + 4X2 ≥ 160
B)4X1 + 8X2 ≤ 160
C)8X1 - 4X2 ≤ 160
D)8X1 + 4X2 ≤ 160
E)4X1 - 8X2 ≤ 160

Question

The feasible region in the diagram below is consistent with which one of the following constraints? 
A)8X1 + 4X2 ≥ 160 
B)4X1 + 8X2 ≤ 160 
C)8X1 - 4X2 ≤ 160 
D)8X1 + 4X2 ≤ 160 
E)4X1 - 8X2 ≤ 160

Quizplus · Accepted Answer

Looking at the graph, we can see that the feasible region is the shaded area. The feasible region includes points that satisfy the constraints, which correspond to the lines that form the boundaries of the shaded area.

Option A: 8X1 + 4X2 ≥ 160 corresponds to a line with a slope of -2 (When X1=0, X2=40 and when X1=20, X2=0). This line doesn't form a boundary of the feasible region.

Option B: 4X1 + 8X2 ≤ 160 corresponds to a line with a slope of -0.5 (when X1=0, X2=20 and when X1=40, X2=0). This line forms one of the boundaries of the feasible region.

Option C: 8X1 - 4X2 ≤ 160 corresponds to a line with a slope of 2 (when X1=0, X2=-40 and when X1=20, X2=0). This line doesn't form a boundary of the feasible region.

Option D: 8X1 + 4X2 ≤ 160 corresponds to a line with a slope of -2 (when X1=0, X2=40 and when X1=20, X2=0). This line forms one of the boundaries of the feasible region.

Option E: 4X1 - 8X2 ≤ 160 corresponds to a line with a slope of 0.5 (when X1=0, X2=-20 and when X1=40, X2=0). This line doesn't form a boundary of the feasible region.

Therefore, the only constraint consistent with the feasible region is D) 8X1 + 4X2 ≤ 160.

The Feasible Region in the Diagram Below Is Consistent with Which