CBSE Class 12 Mathematics Linear Programming Worksheet Set A

CBSE Class 12 Mathematics Linear Programming (1). CBSE issues sample papers every year for students for class 12 board exams. Students should solve the CBSE issued sample papers to understand the pattern of the question paper which will come in class 12 board exams this year. The sample papers have been provided with marking scheme. It’s always recommended to practice as many CBSE sample papers as possible before the board examinations. Sample papers should be always practiced in examination condition at home or school and the student should show the answers to teachers for checking or compare with the answers provided. Students can download the sample papers in pdf format free and score better marks in examinations. Refer to other links too for latest sample papers.

Question. A Linear function, which is minimized or maximized is called
(a) an objective function
(b) an optimal function
(c) A feasible function
(d) None of these
Answer : A

Question. Any feasible solution which maximizes or minimizes the objective function is Called:
(a) A regional feasible solution
(b) An optimal feasible solution
(c) An objective feasible solution
(d) None of these
Answer : B

Question. The maximum value of Z = 3x + 4y subject to the constraints : x+ y ≤ 4, x ≥ 0 , y ≥ 0 is :
(a) 0
(b) 12
(c) 16
(d) 18
Answer : C

Question. The maximum value of 𝑍 = 4𝑥 + 2𝑦 subjected to the Constraints2𝑥 + 3𝑦 ≤ 18 ,𝑥 + 𝑦 ≥ 10 ;𝑥, 𝑦 ≥ 0 is
(a) 320
(b) 300
(c) 230
(d) none of these
Answer : D

Question. The point in the half plane 2𝑥 + 3𝑦 − 12 ≥ 0 is :
(a) (- 7,8 )
(b) ( 7 , - 8 )
(c) ( -7 , - 8 )
(d) (7, 8 )
Answer : D

Question. The solution set of the in equation 2𝑥 + 𝑦 > 5 is
(a) Half plane that contains the origin
(b) Open half plane not containing the origin
(c) Whole 𝑥𝑦 −plane except the points lying on the line 2𝑥 + 𝑦 = 5
(d) None of these
Answer : B

Question. Objective function of a LPP is
(a) a constraint
(b) a function to be optimized
(c) a relation between the variables
(d) none of these
Answer : B

Question. Which of the following statements is correct?
(a) Every L P P admits an optimal solution
(b) A L P P admits unique optimal solution
(c) If a L P P admits two optimal solution solutions, it has aninfinite number of optimal solutions
(d) The set of all feasible solutions of a LPP is a finite set.
Answer : C

Question. The maximum value of Z = 2x +3y subjectto the constraints :
𝑥 + 𝑦 ≤ 1 , 3𝑥 + 𝑦 ≤ 4 , 𝑥, 𝑦 ≥ 0is
(a) 2
(b) 4
(c) 5
(d) 3
Answer : C

Question. The optimal value of the objective function is attained at the points :
(a) Given the intersection of inequations with the axes only
(b) Given by intersection of inequations with X-axis only
(c) Given by corner points of the feasible region
(d) None of these.
Answer : C

CASE STUDY QUESTIONS

I. A company started airlines business and for running business it bought aeroplanes . Now an aeroplane can carry maximum of 200 passengers . A profit of Rs.400 is made on each first class ticket and a profit of Rs.300 is made on each second class ticket . The airline reserves at least 20 seats for first class .However , at least four times as many passengers prefer to travel by second class then by first class . Company wants to make maximum profit by selling tickets of first class (𝑥) and second class (𝑦) .
Using the above information give the answer of the following questions.

Question. To get maximum profit how many first class tickets should be sold –
(a) 20
(b) 180
(c) 160
(d) 40
Answer : D

Question. Corner points of feasible region are
(a) (20,180)
(b) (20,0)
(c) (40,0)
(d) all the above
Answer : D

Question. Difference between the maximum profit and minimum profit is equal to
(a) 8000
(b) 56000
(c) 64000
(d) none of the above
Answer : A

Question. The objective function is
(a) 400𝑥 + 300𝑦
(b) 300𝑥 + 400𝑦
(c) 𝑥 + 𝑦
(d) none of the above
Answer : A

Question. Minimum profit is equal to
(a) 8000
(b) 6000
(c) 64000
(d) none of the above
Answer : A

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