Question

Without graphing, determine which of the points P1=(3,4), P2=(2,−6), P3=(1,3) are part of the feasible set that is a subject to the following constraints:

x+2y≤8
2x−y≥4
​

Answer 1

Only the point P2=(2,−6) satisfies both constraints x + 2y ≤ 8 and 2x - y ≥ 4, making it the only point that is part of the feasible set.

Step-by-step explanation:

To determine which points are part of the feasible set without graphing for the given constraints x + 2y ≤ 8 and 2x - y ≥ 4, we simply plug the values of each point into these inequalities.

• For P1=(3,4):
  3 + 2(4) = 3 + 8 = 11, which is not ≤ 8, so it does not satisfy the first constraint.
  2(3) - 4 = 6 - 4 = 2, which is ≥ 4, so it satisfies the second constraint.
• For P2=(2,−6):
  2 + 2(−6) = 2 - 12 = -10, which is ≤ 8, so it satisfies the first constraint.
  2(2) - (−6) = 4 + 6 = 10, which is ≥ 4, so it satisfies the second constraint.
• For P3=(1,3):
  1 + 2(3) = 1 + 6 = 7, which is ≤ 8, so it satisfies the first constraint.
  2(1) - 3 = 2 - 3 = -1, which is not ≥ 4, so it does not satisfy the second constraint.

Thus, the only point that satisfies both constraints and is part of the feasible set is P2=(2,−6).