Question

APPLICATION
Cite five (5) evidences in your own in different real-life situations about inequalities?​

Answer 1

Step-by-step explanation:

5.7 Real-World Applications of Systems of Inequalities

Difficulty Level: Basic | Created by: CK-12

Last Modified: Dec 24, 2014

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The Vertex Theorem for Feasible Regions

Introduction

In this lesson you will learn about the vertex theorem for feasible regions and how to apply this theorem to real-world problems. You will learn to write a system of linear inequalities to model the real-world problem. This system will then be graphed to determine the solution set for the system of inequalities. Using the vertex theorem, you will then answer the real-world problem.

Objectives

The lesson objectives for the Vertex Theorem for Feasible Regions are:

Understanding the vertex theorem.

Writing a system of inequalities for a real-world problem.

Solving the system of inequalities by graphing

Determining the vertices algebraically by solving the linear inequalities.

Using the vertex theorem to determine the answer to the real-world problem.

Introduction

A system of linear inequalities is often used to determine the best solution to a problem. This solution could be as simple as determining how many of a product should be produced to maximize a profit or as complicated as determining the correct combination of drugs to give a patient. Regardless of the problem, there is a theorem in mathematics that is used, with a system of linear inequalities, to determine the best solution to the problem.

Guidance

The following diagram shows a feasible region that is within a polygonal region.

The linear function

z=2x+3y

will now be evaluated for each of the vertices of the polygon.

To evaluate the value of ‘

z

’ substitute the coordinates of the point into the expression for ‘

x

’ and ‘

y

’.

(0,0)(0,4)(6,0)(3,6)(9,4)z=2x+3y→z=2(0)+3(0)→z=0+0→z=0Therefore 2x+3y=0z=2x+3y→z=2(0)+3(4)→z=0+12→z=12Therefore 2x+3y=12z=2x+3y→z=2(6)+3(0)→z=12+0→z=12Therefore 2x+3y=12z=2x+3y→z=2(3)+3(6)→z=6+18→z=24Therefore 2x+3y=24z=2x+3y→z=2(9)+3(4)→z=18+12→z=30Therefore 2x+3y=30