Question

Which of the following is not a vertex of the positive region bounded by the inequalities

2x+3y ≤ 6, 5x+3y ≤ 15 and x,y ≥ 0?
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Answer 1

Correct option is D) All of these

Step-by-step explanation:

Step 1 of 4

To see whether the given option is a vertex of the positive region bounded by the inequalities, put the options in the inequalities.

Step 2 of 4

Putting (0,2) in inequalities

• 2x+3y≤6 = 2(0) + 3(2)≤6 ⇒ 6≤6
• 5x+3y≤15 = 5(0) + 3(2) ≤15 ⇒6≤15
• x,y≥0  =  2≥ 0

Step 3 of 4

Putting (0,0) in ineuqlities

• 2x+3y≤6 = 2(0) + 3(0)≤6 ⇒ 0≤6
• 5x+3y≤15 = 5(0) + 3(0) ≤15 ⇒ 0≤15
• x,y≥0  =  0 ≥ 0

Step 4 of 4

Putting (3,0) in ineuqlities

• 2x+3y≤6 = 2(3) + 3(0)≤6 ⇒ 6≤6
• 5x+3y≤15 = 5(3) + 3(0) ≤15 ⇒ 15≤15
• x,y≥0  =  3 ≥ 0

Final Answer

Therefore, D) all of these is correct

Complete question is

Which of the following is not a vertex of the positive region bounded by the inequalities 2x+3y≤6,5x+3y≤15 and x,y≥0

a) (0, 2)

b) (0, 0)

c) (3, 0)

d) All of these