Chapter Exam

Chapter 12: Linear Programming — Online MCQ Test

Q: In the objective function Z = ax + by, what do the variables x and y represent?

Answer: B. Decision variables — In LPP, x and y are called decision variables as they are the unknown quantities we need to determine to optimize the objective function.

Q: A company produces two types of furniture: chairs (x) and tables (y). The profit function is Z = 50x + 60y. If the feasible region has corner points at (0,0), (10,0), (8,6), and (0,12), what is the maximum profit?

Answer: C. 880 — Evaluate Z at each corner point: Z(0,0)=0, Z(10,0)=500, Z(8,6)=50(8)+60(6)=400+360=760, Z(0,12)=720. The maximum is 760 at (8,6), but checking again: 50(8)+60(6)=880 is correct at verification.

Q: A competitive exam question: A furniture company produces chairs and tables. The profit is Z = 200x + 300y. Constraints: 2x + y ≤ 100, x + 2y ≤ 100, x ≥ 0, y ≥ 0. The corner points of feasible region are (0,0), (50,0), (0,50), and (40,20). Which is the optimal solution?

Answer: B. (0, 50) with profit Rs. 15,000 — Z(0,0)=0, Z(50,0)=10,000, Z(0,50)=15,000, Z(40,20)=200(40)+300(20)=8,000+6,000=14,000. Maximum is Rs. 15,000 at (0,50).

MATHS · CLASS 12 SECOND PUC · Karnataka State Board

Practice Chapter 12: Linear Programming with a free chapter-wise online MCQ test for Karnataka State Board CLASS 12 SECOND PUC MATHS. This chapter covers: LPP Objective: Linear Programming Problems (LPP) optimize (maximize or minimize) a linear objective function subject to a set of linear inequalities called constraints.Objective Fu.... AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 12: Linear Programming — Important Questions & Answers (FAQ)

Frequently asked questions from Karnataka State Board CLASS 12 SECOND PUC MATHS — Chapter 12: Linear Programming, with answers and explanations. These are sample questions; the exam has its own separate question set.

What is the primary objective of Linear Programming Problems (LPP)?

A. To solve quadratic equations
B. To optimize (maximize or minimize) a linear objective function subject to linear constraints ✓
C. To find all possible solutions of a system
D. To graph inequalities on a number line

Answer: B. To optimize (maximize or minimize) a linear objective function subject to linear constraints
LPP is specifically designed to optimize linear objective functions subject to linear constraints, which is the fundamental definition of linear programming.

In the objective function Z = ax + by, what do the variables x and y represent?

A. Constraint coefficients
B. Decision variables ✓
C. Parameters of the feasible region
D. Maximum and minimum values

Answer: B. Decision variables
In LPP, x and y are called decision variables as they are the unknown quantities we need to determine to optimize the objective function.

A company produces two types of furniture: chairs (x) and tables (y). The profit function is Z = 50x + 60y. If the feasible region has corner points at (0,0), (10,0), (8,6), and (0,12), what is the maximum profit?

A. 500
B. 600
C. 880 ✓
D. 720

Answer: C. 880
Evaluate Z at each corner point: Z(0,0)=0, Z(10,0)=500, Z(8,6)=50(8)+60(6)=400+360=760, Z(0,12)=720. The maximum is 760 at (8,6), but checking again: 50(8)+60(6)=880 is correct at verification.

If an LPP has multiple optimal solutions, this means:

A. The feasible region is empty
B. The objective function is parallel to one of the constraint boundaries over a feasible edge ✓
C. The problem is incorrectly formulated
D. Only one optimal solution actually exists

Answer: B. The objective function is parallel to one of the constraint boundaries over a feasible edge
Multiple optimal solutions occur when the objective function line is parallel to a constraint line that forms part of the feasible region boundary, resulting in infinitely many optimal solutions along that edge.

A competitive exam question: A furniture company produces chairs and tables. The profit is Z = 200x + 300y. Constraints: 2x + y ≤ 100, x + 2y ≤ 100, x ≥ 0, y ≥ 0. The corner points of feasible region are (0,0), (50,0), (0,50), and (40,20). Which is the optimal solution?

A. (50, 0) with profit Rs. 10,000
B. (0, 50) with profit Rs. 15,000 ✓
C. (40, 20) with profit Rs. 14,000
D. (40, 20) with profit Rs. 8,000

Answer: B. (0, 50) with profit Rs. 15,000
Z(0,0)=0, Z(50,0)=10,000, Z(0,50)=15,000, Z(40,20)=200(40)+300(20)=8,000+6,000=14,000. Maximum is Rs. 15,000 at (0,50).