Algebra

Linear Programming

Medium

common

Which of the following terms are associated with a linear programming problem?

(A) Constraints

(B) Independent events

(C) Feasible region

(D) Objective function

Choose the correct answer from the options given below:

(A) and (C) only

(A), (C) and (D) only

(B), (C) and (D) only

(A), (B) and (D) only

✅ Correct Option: 2

Linear Programming is a mathematical method used to find the best outcome (like maximum profit or minimum cost) when there are certain limitations.

(A) Constraints

These are rules or limitations that must be followed.

Example: If making products, constraints could be:

Only 100 hours of labor available
Only $5000 budget available

Constraints are a fundamental component of every linear programming problem.

(B) Independent Events

This is a probability concept where one event doesn't affect another event.

Example: Flipping a coin and rolling a dice are independent events.

Independent events belong to probability and statistics, not linear programming.

The area on a graph where all constraints are satisfied simultaneously. It represents all possible solutions that follow the given rules.

The feasible region is essential in solving linear programming problems.

(D) Objective Function

The main goal to be achieved - the function to maximize or minimize.

Examples:

Maximize profit: $5x + 3y$
Minimize cost: $2x + 4y$

Every linear programming problem has an objective function.

Terms associated with Linear Programming:

(A) Constraints ✓
(C) Feasible region ✓
(D) Objective function ✓

(B) Independent events is not associated with linear programming.

Correct Answer: (A), (C) and (D) only

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In linear programming, the optimal value of the objective function is attained at the points given by

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For the graph of a linear programming problem(LPP) given below. If $\min z = 3x+5y$ is the objective function and shaded portion in the figure is the feasible region of the LPP, then constraints other than $x, y \geq 0$ are

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The maximum profit per week is :

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The corner points of the bounded feasible region for an L.P.P are (0, 10), (5, 5), (15,15), and (0, 20). If the objective function is $Z=px+qy, p,q>0$ , then the condition on $p$ and $q$ so that the maximum of $Z$ occurs at (15, 15) and (0, 20) is

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In a linear programming problem, the constraints on decision variables $x$ and $y$ are $y-2x \leq 0$ , $y \geq 0$ , $0 \leq x \leq 5$ . The feasible region of the above problem:

Which of the following terms are associated with a linear programming problem? (A) Constraints (B) Independent events (C) Feasible region (D) Objective function Choose the correct answer from the options given below:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Which of the following terms are associated with a linear programming problem?

(A) Constraints

(B) Independent events

(C) Feasible region

(D) Objective function

Choose the correct answer from the options given below: