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Vidaara.orgClass 12 · Mathematics
CodeVID-M12-12-FRM-01
Formulating an LPP — Assignment
Chapter: Linear Programming
Topic: Formulating a Linear Programming Problem
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.
The function to be optimised in an LPP is the:
  • A.constraint
  • B.objective function
  • C.feasible region
  • D.corner point
2.
Non-negativity restrictions are:
  • A.$x,y\le0$
  • B.$x,y\ge0$
  • C.$x=y$
  • D.$x+y=0$
3.
"At most 40 hours available" translates to:
  • A.$\ge40$
  • B.$=40$
  • C.$\le40$
  • D.$>40$
4.
Decision variables in an LPP represent:
  • A.the profit
  • B.quantities you control
  • C.the constraints
  • D.the optimum
5.
The feasible region is the set of points satisfying:
  • A.the objective
  • B.all the constraints
  • C.one constraint
  • D.none
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.
Each chair needs $1$ h and each table $3$ h of labour; at most $90$ h are available. Write the constraint.
8.
State the non-negativity restrictions for an LPP in $x,y$.
9.
Write the constraint for "produce at least $5$ units of $x$".
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.
A diet needs at least $8$ units of protein; food A gives $2$/unit and B gives $4$/unit. Write the protein constraint.
12.
Define the feasible region of an LPP.
13.
A factory has $12$ h machine time; product $x$ needs $2$ h, $y$ needs $3$ h. Write the constraint.
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.
A manufacturer makes $x$ of item P (profit $\textsf{Rs }5$) and $y$ of Q (profit $\textsf{Rs }3$). P needs $3$ h and Q $2$ h (total $\le60$ h); P needs $1$ and Q $2$ units of material (total $\le40$). Formulate the LPP.

Answer Key

Section A — Multiple Choice Questions
  1. (B) objective function
  2. (B) $x,y\ge0$
  3. (C) $\le40$
  4. (B) quantities you control
  5. (B) all the constraints
Section B — Short Answer (2 marks)
  1. Maximise $Z=50x+80y$.
  2. $x+3y\le90$.
  3. $x\ge0,\ y\ge0$.
  4. $x\ge5$.
Section C — Short Answer (3 marks)
  1. Max $Z=40x+30y$ s.t. $x+y\le12,\ 2x+y\le16,\ x,y\ge0$.
  2. $2x+4y\ge8$.
  3. The set of all points satisfying every constraint (including $x,y\ge0$).
  4. $2x+3y\le12$.
Section D — Long Answer (5 marks)
  1. Max $Z=60x+50y$ s.t. $2x+y\le40,\ x+2y\le50,\ x,y\ge0$.
  2. Max $Z=5x+3y$ s.t. $3x+2y\le60,\ x+2y\le40,\ x,y\ge0$.
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