Consider the following linear programming problem: Maximize 5X + 6Y
Subject to: 4X + 2Y ≤ 420
1X + 2Y ≤ 120
All variables ≥ 0
Which of the following points (X,Y)is feasible?
A)(50,40)
B)(30,50)
C)(60,30)
D)(90,20)

Question

Quizplus · Accepted Answer

To determine feasibility, we need to check if the given points satisfy all the constraints. 
A) (50,40): 
4(50) + 2(40) = 300 ≤ 420 ✔️
1(50) + 2(40) = 130 ≤ 120 ❌
Not feasible as it violates one of the constraints. 
B) (30,50): 
4(30) + 2(50) = 220 ≤ 420 ✔️
1(30) + 2(50) = 130 ≤ 120 ❌
Not feasible as it violates one of the constraints. 
C) (60,30): 
4(60) + 2(30) = 300 ≤ 420 ✔️
1(60) + 2(30) = 120 ≤ 120 ✔️
Feasible as it satisfies all the constraints. 
D) (90,20):
4(90) + 2(20) = 380 ≤ 420 ✔️
1(90) + 2(20) = 130 ≤ 120 ❌
Not feasible as it violates one of the constraints.

Therefore, the only feasible point is (60,30), and it is the best choice as it satisfies all the constraints and maximizes the objective function.

Consider the Following Linear Programming Problem: Maximize 5X + 6Y