For a linear programming problem with the following constraints, which point is in the feasible solution space assuming this is a maximization problem?
14x+6y ≤ 42
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

For a linear programming problem with the following constraints, which point is in the feasible solution space assuming this is a maximization problem? 
14x+6y ≤ 42
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

Quizplus · Accepted Answer

We can check each choice by plugging in the values for x and y into each constraint to see if they satisfy all of the constraints. 
A) 14(1) + 6(5) = 44 > 42 (does not satisfy first constraint)
B) -14 + 1 = -13 > 3 (does not satisfy second constraint)
C) 14(4) + 6(4) = 84 > 42 (does not satisfy first constraint)
D) 14(2) + 6(1) = 34 ≤ 42 (satisfies first constraint)
    2 - 1 = 1 ≤ 3 (satisfies second constraint)
    Therefore, (2,1) is in the feasible solution space. 
E) 14(2) + 6(8) = 80 > 42 (does not satisfy first constraint)
Therefore, the best choice is D, (2,1), as it is the only choice that satisfies both constraints.

For a Linear Programming Problem with the Following Constraints, Which