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

We can determine the feasible region by shading in the area of the graph that satisfies all the constraints. From the graph, we see that the feasible region is above the line 8X1 + 4X2 = 160, below the x-axis, and to the left of the y-axis. This is consistent with constraint D) 8X1 + 4X2 ≤ 160, which can be rearranged as 4X2 ≤ -8X1 + 160 and then divided by 4 on both sides to give us the equation of the line 2X1 + X2 = 40. This line forms the boundary of the feasible region and any point below it satisfies the constraint.

The Feasible Region in the Diagram Below Is Consistent with Which