Linear Inequalities Case Study Questions Class 11 Maths Chapter 5

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Hello students, we are providing case study questions for class 11 Maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 11 Maths. In this article, you will find case study questions for cbse class 11 Maths chapter 5 Linear Inequalities.

Chapter	Linear Inequalities
Type of Questions	Case Study Questions
Nature of Questions	Competency Based Questions
Board	CBSE
Class	11
Subject	Maths
Useful for	Class 12 Studying Students
Answers provided	Yes
Difficulty level	Mentioned
Important Link	Class 11 Maths Chapterwise Case Study

Table of Contents

Case Study Questions on Linear Inequalities

Customised Study Materials for Teachers, Schools and Coaching Institute

Case Study:
A company wants to manufacture and sell pens and pencils. Market research indicates that at most 300 units in total can be produced weekly. Each pen requires ₹20 in production cost and each pencil ₹10. The weekly manufacturing budget does not exceed ₹4,500. The company must make at least 50 pens to meet a contract.

Questions:

Write all the inequalities representing the company’s constraints.
Draw the feasible region (describe its boundaries in words).
What is the maximum number of pencils that can be manufactured? Give the answer with proper justification/calculations.

Solutions:

1. Writing the inequalities:

Let \( x \) = number of pens, \( y \) = number of pencils. \[ \begin{align*} &x + y \leq 300 \\ &20x + 10y \leq 4500 \\ &x \geq 50 \\ &x \geq 0,\ y \geq 0 \end{align*} \]

2. Description of the feasible region:
The solution area lies:

On or below the line \( x + y = 300 \) (total units limit)
On or below the line \( 2x + y = 450 \) (budget constraint, after dividing by 10)
On or to the right of \( x = 50 \) (minimum pens for contract)
Only for non-negative values of \( x, y \) (cannot make negative pens or pencils)

This region on the first quadrant bounded by these lines gives all possible (pen, pencil) combinations possible for the company.

3. Maximum number of pencils producible:

We maximize \( y \) subject to all constraints. Check at intersection points where maximum \( y \) is feasible.

Set \( x = 50 \):
- From \( x + y \leq 300 : y \leq 250 \)
- From \( 2x + y \leq 450 : 2 \times 50 + y \leq 450 \implies y \leq 350 \)
- So, \( y \leq 250 \) (tighter bound)
- Thus, at \( x = 50, y = 250 \) is possible
Check where \( x + y = 300 \) and \( 2x + y = 450 \) intersect:
\[ x + y = 300 \implies y = 300 – x \] \[ 2x + (300 – x) = 450 \implies x + 300 = 450 \implies x = 150 \implies y = 150 \]
At \( x = 150, y = 150 \)
Also see if higher \( y \) possible for other values, but \( y = 250 \) at \( x = 50 \) is highest among vertices.

So, maximum number of pencils is 250 when 50 pens and 250 pencils are made.

We hope the given case study questions for Linear Inequalities Class 11 helps you in your learning.

Also check

Topics from which case study questions may be asked

Introduction to Inequalities
Algebraic Solutions of Linear Inequalities in One Variable
Graphical Representation of Linear Inequalities in One Variable
Solution of System of Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Graphical Solution of Linear Inequalities in Two Variables
Solution of a System of Linear Inequalities in Two Variables

Frequently Asked Questions (FAQs) on Linear Inequalities Case Study Questions

Q1: What is a case study question in mathematics?

A1: A case study question in mathematics is a problem or set of problems based on a real-life scenario or application. It requires students to apply their understanding of mathematical concepts to analyze, interpret, and solve the given situation.

Q2: How should students tackle case study questions in exams?

A2: To tackle case study questions effectively, students should:
Read the problem carefully: Understand the scenario and identify the mathematical concepts involved.
Break down the problem: Divide the case study into smaller parts to manage the information better.
Apply relevant formulas and theorems: Use the appropriate mathematical tools to solve each part of the problem.

Q3: Why are case study questions included in the Class 11 Maths curriculum?

A3: Case study questions are included to bridge the gap between theoretical knowledge and practical application. They help students see the relevance of what they are learning and prepare them for real-life situations where they may need to use these mathematical concepts.

Q4: Are there any online resources or tools available for practicing “Linear Inequalities” case study questions?

A12: We provide case study questions for CBSE Class 11 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.