Consider the following linear programming problem: Which of the following points (X,Y)is not a feasible corner point?
A)(0,60)
B)(105,0)
C)(120,0)
D)(100,10)
E)None of the above

Question

Consider the following linear programming problem:  Which of the following points (X,Y)is not a feasible corner point?
A)(0,60) 
B)(105,0) 
C)(120,0) 
D)(100,10) 
E)None of the above

Quizplus · Accepted Answer

A feasible corner point is a point where all of the constraints are satisfied with equality. 
For the given problem, the constraints are as follows:
X + Y ≤ 120
X ≤ 105
Y ≤ 60
X, Y ≥ 0

We can check each point to see which ones satisfy all of the constraints as equalities.

A) (0,60): 
0 + 60 = 60 ≤ 120 (satisfied)
0 ≤ 105 (satisfied)
60 ≤ 60 (satisfied)
Both X and Y are ≥ 0 (satisfied)
All constraints are satisfied.

B) (105,0): 
105 + 0 = 105 ≤ 120 (satisfied)
105 ≤ 105 (satisfied)
0 ≤ 60 (satisfied)
Both X and Y are ≥ 0 (satisfied)
All constraints are satisfied.

C) (120,0): 
120 + 0 = 120 ≤ 120 (satisfied)
120 > 105 (not satisfied)
0 ≤ 60 (satisfied)
Both X and Y are ≥ 0 (satisfied)
One of the constraints (X ≤ 105) is not satisfied.

D) (100,10): 
100 + 10 = 110 ≤ 120 (satisfied)
100 ≤ 105 (satisfied)
10 ≤ 60 (satisfied)
Both X and Y are ≥ 0 (satisfied)
All constraints are satisfied.

Therefore, the only point that is not a feasible corner point is C) (120,0).

Consider the Following Linear Programming Problem: Which of the Following