For the following constraints, which point is in the feasible region of this minimization problem? (1) 14x + 6y ≥ 42 (2) x - y ≥ 5
A) x = -1, y = 1
B) x = 0, y = 4
C) x = 2, y = 1
D) x = 5, y = 1
E) x = 6, y = 0

Question

Quizplus · Accepted Answer

We need to find the feasible region for the given constraints. For constraint 1, we can re-write it as 7x + 3y ≥ 21. This means any point (x,y) that satisfies this equation lies on or above the line 7x + 3y = 21. For constraint 2, any point (x,y) that satisfies this equation lies on or above the line x - y = 5.

We can plot these two lines to get the feasible region as shown below:

Feasible Region Image: https://i.imgur.com/PbZSoz0.png

The shaded region represents the feasible region of the problem. We need to find which point lies in this region.

Option A) (-1,1) is clearly outside the feasible region.
Option B) (0,4) is also clearly outside the feasible region.
Option C) (2,1) is inside the feasible region.
Option D) (5,1) is outside the feasible region.
Option E) (6,0) is inside the feasible region.

Therefore, the only point that lies in the feasible region is E) (6,0).

For the Following Constraints, Which Point Is in the Feasible