For the constraints given below,which point is in the feasible solution space of this maximization problem?
(1)14x + 6y ≤ 42
(2)x - y ≤ 3
A) x = 1, y = 5
B) x = -1, y = 1
C) x = 4, y = 4
D) x = 2, y = 1
E) x = 2, y = 8

Question

Quizplus · Accepted Answer

To determine if a point is in the feasible solution space, we need to ensure that it satisfies both constraints:
(1) 14x + 6y ≤ 42
(2) x - y ≤ 3
Plugging in the values for each option, we get:
A) 14(1) + 6(5) = 44, which violates constraint (1)
B) (-1) - 1 = -2, which satisfies both constraints
C) 14(4) + 6(4) = 84, which violates constraint (1)
D) 14(2) + 6(1) = 34, and 2 - 1 = 1, both satisfy both constraints
E) 14(2) + 6(8) = 92, which violates constraint (1)

Therefore, only option D satisfies both constraints and is in the feasible solution space.

For the Constraints Given Below,which Point Is in the Feasible