BITSAT Mathematics Linear Programming MCQs

Question: The maximum value of z = 3x + 2y subject to x + 2y≥ 2, x + 2y ≤ 8, x, y ≥ 0 is :

• a) 32
• b) 24
• c) 40
• d) None of these

Answer: 24

Question: Minimise  

Subject to

is a LPP with number of constraints 

• a) m – n
• b) mn
• c) m + n
• d) m/n

Answer: m + n

Question: Consider

Then number of possible solutions are :

• a) Zero
• b) Unique
• c) Infinite
• d) None of these

Answer: Infinite

Question: A shopkeeper wants to purchase two article A and B of cost price ₹ 4 and 3 respectively. He thought that he may earn 30 paise by selling article A and 10 paise by selling article B. He has not to purchase total article worth more than ₹ 24. If he purchases the number of articles of A and B, x and y respectively, then linear constraints are

• a) x ≥ 0, y≤ 0, 4x +3 y ≥ 24
• b) x ≥ 0, y ≥ 0, 30x + 10 y ≤ 24
• c) x ≥ 0, y ≥ 0, 4x +3 y ≥ 24
• d) x ≥ 0, y ≥0, 30x +40 y ≥ 24

Answer: x ≥ 0, y≤ 0, 4x +3 y ≥ 24

Question: Prabhat wants to invest the total amount of ₹ 15,000 in saving certificates and national saving bonds. According to rules, he has to invest at least ₹ 2000 in saving certificates and ₹ 2500 in national saving bonds. The interest rate is 8% on saving certificate and 10% on national saving bonds per annum. He invest ₹ x in saving certificate and ₹ y in national saving bonds. Then the objective function for this problem is

• a) 0.08 x + 0.10 y
• b)

  

• c) 2000x + 2500 y
• d)

  

Answer: 0.08 x + 0.10 y

Question: For the constraints of a L.P. Problem given by x₁ + 2x₂ ≤ 2000, x1 + x₂ ≤ 1500 and x ₂ ≤ 600 and x₁, x₂ ≥ 0, which one of the following points does not lie in the positive bounded region

• a) (1000, 0)
• b) (0, 500)
• c) (2, 0)
• d) (2000, 0)

Answer: (2000, 0)

Question:  A wholesale merchant wants to start the business of cereal with  ₹24000. Wheat is ₹400 per quintal and rice is ₹600 per quintal. He has capacity to store 200 quintal cereal. He earns the profit₹25 per quintal on wheat and ₹40 per quintal on rice. If he store x quintal rice and y quintal wheat, then for maximum profit the objective function is

• a) 25 x + 40 y
• b) 40x + 25 y
• c) 400x + 600y
• d)

  

Answer: 40x + 25 y

Question: The minimum value of the function z = 4x + 3y subject to the constraints 3x + 2y ≥ 160, 5x + 2y ≥ 200, x + 2y ³ 80, x ≥ 0, y ≥ 0 is

• a) 320
• b) 300
• c) 220
• d) 200

Answer: 220

Question: The constraints –x₁ + x₂ ≤ 1, –x₁ +3x₂ ≤ 9, x₁,x₂ ≥ 0 define on

• a) Bounded feasible space.
• b) Unbounded feasible space
• c) Both bounded and unbounded feasible space.
• d) None of these

Answer: Unbounded feasible space

Question: The maximum value of z = 3x + 4y subject to the constraints x + y ≤ 40, x + 2y ≤ 60, x ≥ 0, y ≥ 0 is

• a) 120
• b) 140
• c) 100
• d) 160

Answer: 140

Question: The maximum value of z = 3x + 4y subject to the condition x + y ≤ 40 , x + 2y ≤ 60, x,y ≥ 0 is

• a) 130
• b) 120
• c) 40
• d) 140

Answer: 140

Question: The point at which the maximum value of ( 3x + 2y) subject to the constraints x + y ≤ 2, x ≥ 0, y ≥0 is obtained, is

• a) (0, 0)
• b) (1.5, 1.5)
• c) (2, 0)
• d) (0, 2)

Answer: (2, 0)

Question: The solution set of constraints x + 2y ≥ 11, 3x + 4y ≤ 30, 2x + 5y ≤ 30 and x ≥ 0 , y ≥ 0 , includes the point

• a) (2, 3)
• b) (3, 2)
• c) (3, 4)
• d) (4, 3)

Answer: (3, 4)

Question: The maximum value of z = 3x + 2y subject to x + 2y≥ 2, x + 2y ≤ 8, x, y ≥ 0 is :

• a) 32
• b) 24
• c) 40
• d) None of these

Answer: 24

Question: Minimise  

Subject to 

is a LPP with number of constraints 

• a) m – n
• b) mn
• c) m + n
• d)

  

Answer: m + n