← Back to chapter
Vidaara.orgClass 12 · Mathematics
CodeVID-M12-12-CT
Linear Programming — Full Chapter Test
Chapter: Linear Programming
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
The function to be optimised in an LPP is the:
  • A.constraint
  • B.objective function
  • C.feasible region
  • D.corner point
2.
By the corner-point theorem, the optimum occurs at:
  • A.the centre
  • B.a corner point
  • C.the origin always
  • D.any interior point
3.
Non-negativity restrictions are:
  • A.$x,y\le0$
  • B.$x,y\ge0$
  • C.$x=y$
  • D.$x+y=0$
4.
Maximum of $Z=3x+2y$ over $\{(0,0),(4,0),(0,5),(2,3)\}$ is:
  • A.$10$
  • B.$12$
  • C.$6$
  • D.$0$
5.
"At most 40 hours available" translates to:
  • A.$\ge40$
  • B.$=40$
  • C.$\le40$
  • D.$>40$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
A firm makes $x$ chairs and $y$ tables with profit $\textsf{Rs }50$ and $\textsf{Rs }80$. Write the objective function.
7.
Find the maximum of $Z=x+y$ over the corners $(0,0),(2,0),(0,3)$.
8.
Each chair needs $1$ h and each table $3$ h of labour; at most $90$ h are available. Write the constraint.
9.
Find the minimum of $Z=2x+3y$ over $(1,0),(0,1)$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Write the full LPP: maximise profit $40x+30y$ subject to $x+y\le12$ and $2x+y\le16$.
11.
Maximise $Z=3x+2y$ over corners $(0,0),(4,0),(0,5),(2,3)$.
12.
A diet needs at least $8$ units of protein; food A gives $2$/unit and B gives $4$/unit. Write the protein constraint.
13.
Minimise $Z=x+y$ over corners $(2,0),(0,3),(1,1)$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A company makes products A and B. Each A gives profit $\textsf{Rs }60$ (needs $2$ h machine, $1$ h labour); each B gives $\textsf{Rs }50$ (needs $1$ h machine, $2$ h labour). Machine $\le40$ h, labour $\le50$ h. Formulate the LPP.
15.
Solve graphically: maximise $Z=4x+3y$ subject to $x+y\le4,\ x\ge0,\ y\ge0$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) objective function
  2. (B) a corner point
  3. (B) $x,y\ge0$
  4. (B) $12$
  5. (C) $\le40$
Section B — Short Answer (2 marks)
  1. Maximise $Z=50x+80y$.
  2. $3$.
  3. $x+3y\le90$.
  4. $2$.
Section C — Short Answer (3 marks)
  1. Max $Z=40x+30y$ s.t. $x+y\le12,\ 2x+y\le16,\ x,y\ge0$.
  2. $12$.
  3. $2x+4y\ge8$.
  4. $2$.
Section D — Long Answer (5 marks)
  1. Max $Z=60x+50y$ s.t. $2x+y\le40,\ x+2y\le50,\ x,y\ge0$.
  2. Maximum $Z=16$ at $(4,0)$.
Generated by Vidaara.org · Assignment VID-M12-12-CT · vidaara.org