6. Systems of Equations and Inequalities

Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

Linear Programming

Writing Constraints and Objective Functions

Linear Programming Example

Write Objective Function

Linear Programming - Example 2

Using Linear Programming to Solve Real World Problems with Constraints

In Exercises 1–4, find the value of the objective function at each corner of the graphed region. What is the maximum value of the objective function? What is the minimum value of the objective function? 1. Objective Function z=5x+6y <img src="https://lightcat-files.s3.amazonaws.com/problem_images/dc2efa2c0487378a-1675712281686.jpg" alt="" />

Write an Objective Function

Linear Programming (intro -- defining variables, constraints, objective function)

Find the value of the objective function z = 2x + 3y at each corner of the graphed region shown. What is the maximum value of the objective function? What is the minimum value of the objective function? <img src="https://lightcat-files.s3.amazonaws.com/problem_images/56a556cd8ac93ad1-1672429065205.jpg" alt="" />

In Exercises 1–4, find the value of the objective function at each corner of the graphed region. What is the maximum value of the objective function? What is the minimum value of the objective function? 1. Objective Function z=40x+50y <img src="https://lightcat-files.s3.amazonaws.com/problem_images/be2ea4a5a1245d47-1675713088491.jpg" alt="" />

In Exercises 5–14, an objective function and a system of linear inequalities representing constraints are given.
a. Graph the system of inequalities representing the constraints. 
b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/173928493afbadf4-1670240107772.jpg" alt="" />

In Exercises 5–14, an objective function and a system of linear inequalities representing constraints are given.
a. Graph the system of inequalities representing the constraints. 
b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.

In Exercises 5–14, an objective function and a system of linear inequalities representing constraints are given.
a. Graph the system of inequalities representing the constraints. 
b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/ba8597a53598665b-1670220931006.jpg" alt="" />

In Exercises 57–59, graph the region determined by the constraints. Then find the maximum value of the given objective function, subject to the constraints.  This  is a piecewise function. Refer to the textbook.

Linear Programming Word Problem - Example 1

Linear Programming 2: Graphical Solution - Minimization Problem

Represent constraints created by a system of inequalities

In Exercises 5–14, an objective function and a system of linear inequalities representing constraints are given.
a. Graph the system of inequalities representing the constraints. 
b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/d64180540da3ff05-1670224704450.jpg" alt="" />

In Exercises 5–14, an objective function and a system of linear inequalities representing constraints are given.
a. Graph the system of inequalities representing the constraints. 
b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/51c919016b3188dc-1670242675926.jpg" alt="" />

Represent constraints on solutions using systems of linear inequalities

Represent solutions and constraints to systems of linear inequalities by graphing

Learn the toughest concepts covered in Algebra with step-by-step video tutorials and practice problems by world-class tutors

College Algebra

https://static.studychannel.pearsonprd.tech/courses/college-algebra/thumbnails/college-algebra

#FFFFFF

patrickJMT

victoriamiles

Kim Haughee's Mathematics Channel

Mario's Math Tutoring

LearnZillion

Joshua Emmanuel

MATHfisch

Jon Anderson

Kimberly Brehm

1. Fundamental Concepts of Algebra

2. Equations and Inequalities

3. Functions and Graphs

4. Polynomial and Rational Functions

5. Exponential and Logarithmic Functions

7. Matrices and Determinants

8. Conic Sections

9. Sequences, Induction, and Probability

undefined - Channels

Graph a Linear Inequality in Two Variables

Graph a Nonlinear Inequality in Two Variables

Use Mathematical Models Involving Linear Inequalities

Graph a System of Inequalities

Systems of Inequalities

Determine Whether an Ordered Pair is a Solution of a Linear System

Solve Linear Systems by Substitution

Solve Linear Systems by Addition

Identify Systems That Don't Have One Ordered-Pair Solution

Solve Problems Using Systems of Linear Equations

Systems of Linear Equations in Two Variables

Use Inequalities to Describe Limitations in a Situation

Use Linear Programming to Solve Problems

Decompose P / Q, Where Q Has Only Distinct Linear Factors

Decompose P / Q, Where Q Has Repeated Linear Factors

Decompose P / Q, Where Q Has a Nonrepeated Prime Quadratic Factor

Decompose P / Q, Where Q Has a Prime, Repeated Quadratic Factor

Partial Fractions

Recognize Systems of Nonlinear Equations in Two Variables

Solve Nonlinear Systems by Substitution

Solve Nonlinear Systems by Addition

Solve Problems Using Systems of Nonlinear Equations

Systems of Nonlinear Equations in Two Variables

Verify Solution of a System of Linear Equations in 3 Variables

Solve Systems of Linear Equations in Three Variables

Solve Problems Using Systems in 3 Variables

Systems of Linear Equations in 3 Variables

General Chemistry

Jules

Study the key concepts of Physics with descriptive videos, questions, and more

Physics

Patrick

General Biology

Jason

Financial Accounting

Brian

Dive deep into Psychology with videos, practice problems, and more.

Psychology

Microeconomics

The first in a two-course sequence introduces the basic structure and functions of the human body

Anatomy & Physiology

College Algebra covers algebraic topics and skills necessary to succeed in college-level math

Organic Chemistry

Johnny

Genetics

Kylia

GOB Chemistry

Microbiology

Cell Biology

Analytical Chemistry

Study topics incliding trogonometric functions, identities and equations, solutions of triangles, complex numbers, and other topics as time permits

Trigonometry

Learn the toughest concepts covered in Precalculus with step-by-step video tutorials and practice problems by world-class tutors

Precalculus

Biochemistry

Macroeconomics

Chemistry

Biology

Math

Business

Social Sciences

Michelle Barry Franco

Building Great Presentations

Eric Zackrison, PhD

Critical Thinking And Problem Solving

Sam Bennett

Embracing Times Of Uncertainty

Nicole Tetreault, PhD

Emotional Intelligence Basics

Eugene Choi, PharmD

Enhancing Your Critical Thinking Skills

Jason Richardson, PsyD

Habits To Win Every Day

Alyssa Lowery, PhD

Having Powerful Advanced Conversations

Don Gilman, EdD

How To Influence & Persuade

Amy Matthews

Leadership Skills For Rising Stars

Listening To Lead

Michael Shermer, PhD

Making Decisions Under Uncertainty

Lynne Hurdle

Mistakes To Avoid When Resolving Conflict

Michael Veltri

Overcoming Decision Making Traps

Mike Vardy

Prioritizing Effectively

Secrets Of Effective Prioritization

Strategies To Build Up Your Creativity

Tools For Decision Making

Tutti Taygerly

Unleash And Advance Your Creativity

Winning Collaboration: How To Work More Effectively With Different Personalities

Writing Emails People Want To Read

Critical Thinking

Self Management

Digital Literacy

Collaboration

Communication

Analytical Thinking

Leadership

Flexibility/Adaptability

Innovation

Eric Zackrison

Nicole Tetreault

Dive deep into Python with videos and more.

Introduction to Python

Arianne Dee

Agile Project and Product Management

Agile & Product Management

Mariya Breyther 

Introduction to Microsoft Power BI

Microsoft Power BI

Chris Sorensen

Data Analysis Fundamentals with Excel

Data Analysis - Excel

Chris Sorensen & Ammul Shergill

Getting Started with  and Cryptocurrency

Introduction to Blockchain

George Levy

Learn Enough HTML, CSS and Layout to be Dangerous

HTML, CSS & Layout

Lee Donahoe & Michael Hartl

Learn Enough JavaScript to be Dangerous: A Tutorial Introduction to Programming with JavaScript