Question

Examine the LP formula shown below. I have already graphed the axes and the feasible region but I have not identified the constraints. This appears in Figure 1 – note that the feasible region is the 5-sided polygon formed by the corner (extreme) points labeled A, B, C, D, and E. However, you will still have to construct and move the objective function line (when provided) in order to find the optimal solution. Subject to: 2X + 3Y < 50 2X + Y < 30 - X +2Y < 18 X > 4 X ≥ 0 and Y ≥ 0 Figure 1: Coordinate Axes and Feasible Region for LP Problem Y-AXIS

What is the Constraint defined by the points A and B in the feasible region shown in Figure 1?
Group of answer choices
a)y>=0
b)2x+3y<=50
c)2x+y<=30
d)-x+2y<=18
e)x>=4

Answer 1

The constraint line between points A and B in the Linear Programming problem graph corresponds to the inequality '2X + 3Y ≤ 50', which is option (b).

Step-by-step explanation:

The student asked about identifying the constraint defined by points A and B in a Linear Programming (LP) problem. If A and B are two adjacent corner points of the feasible region on the coordinate graph, and the feasible region is where all constraints are satisfied, then the constraint line involving A and B will be one of the edges of the feasible region. Therefore, we can rule out the y ≥ 0 and x ≥ 0 options as they represent the axes constraints, not the line segment between two points in the feasible region. The constraint “2X + 3Y ≤ 50” defines an edge of the feasible region that is not coinciding with the axes, so it's the likely candidate for the constraint between A and B, hence correct choice (b).