The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*.

-The equation for constraint DH is:
A) 4X + 8Y ≥ 32
B) 8X + 4Y ≥ 32
C) X + 2Y ≥ 8
D) 2X + Y ≥ 8

Question

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*.
 
-The equation for constraint DH is:
A) 4X + 8Y ≥ 32 
B) 8X + 4Y ≥ 32 
C) X + 2Y ≥ 8 
D) 2X + Y ≥ 8

Quizplus · Accepted Answer

Constraint DH passes through points (0, 4) and (8, 0). We can find the equation of this line by using the slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept. The slope is:

m = (0 - 4)/(8 - 0) = -1/2

To find the y-intercept, we can substitute one of the points:

4 = -1/2(0) + b
b = 4

So the equation for DH is:

y = -1/2x + 4

To write this in the form of an inequality, we just need to make sure that all points on or below this line satisfy the constraint. We can rewrite the inequality as:

x + 2y ≥ 8

This matches choice C.

The Following Is a Graph of a Linear Programming Problem