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Vidaara.orgClass 12 · Mathematics
CodeVID-M12-12-GRP-01
Graphical Solution of an LPP — Assignment
Chapter: Linear Programming
Topic: Graphical Solution & the Corner-Point Method
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • 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.
By the corner-point theorem, the optimum occurs at:
  • A.the centre
  • B.a corner point
  • C.the origin always
  • D.any interior point
2.
Maximum of $Z=3x+2y$ over $\{(0,0),(4,0),(0,5),(2,3)\}$ is:
  • A.$10$
  • B.$12$
  • C.$6$
  • D.$0$
3.
The feasible region of an LPP is always:
  • A.a circle
  • B.convex
  • C.unbounded
  • D.a single point
4.
If the feasible region is bounded, then:
  • A.only a max exists
  • B.both max and min exist
  • C.no optimum exists
  • D.only a min exists
5.
Corner points of a feasible region are its:
  • A.interior points
  • B.vertices
  • C.edges
  • D.centre
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the maximum of $Z=x+y$ over the corners $(0,0),(2,0),(0,3)$.
7.
Find the minimum of $Z=2x+3y$ over $(1,0),(0,1)$.
8.
Where does the optimum of a bounded LPP occur?
9.
Find the corner point common to $x+y=4$ and $x=y$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Maximise $Z=3x+2y$ over corners $(0,0),(4,0),(0,5),(2,3)$.
11.
Minimise $Z=x+y$ over corners $(2,0),(0,3),(1,1)$.
12.
Find the corner points of the region $x\ge0,\ y\ge0,\ x+y\le4$.
13.
Maximise $Z=5x+3y$ over corners $(0,0),(4,0),(0,3)$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Solve graphically: maximise $Z=4x+3y$ subject to $x+y\le4,\ x\ge0,\ y\ge0$.
15.
Minimise $Z=200x+500y$ subject to $x+2y\ge10,\ 3x+4y\le24,\ x,y\ge0$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) a corner point
  2. (B) $12$
  3. (B) convex
  4. (B) both max and min exist
  5. (B) vertices
Section B — Short Answer (2 marks)
  1. $3$.
  2. $2$.
  3. At a corner point.
  4. $(2,2)$.
Section C — Short Answer (3 marks)
  1. $12$.
  2. $2$.
  3. $(0,0),(4,0),(0,4)$.
  4. $20$ (at $(4,0)$).
Section D — Long Answer (5 marks)
  1. Maximum $Z=16$ at $(4,0)$.
  2. Minimum $Z=2300$ at $(4,3)$.
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