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MODULE 5 - LINEAR PROGRAMMING
REVIEW OF LINEAR INEQUALITIES
- Linear equation - an equation that can be written in the form ax + by = c, where a, b, and c are constants and x and y are variables . Note that its graph is a line and it usually uses the slope-intercept formula y = mx + b, where m is the slope and b is the y-intercept.
- Linear inequality - an equation that can be written in the form ax + by < c (or with >, ≤, or ≥ ).
LINEAR PROGRAMMING
Linear programming is a method for solving problems in which a quantity is to be maximized or minimized, when that quantity is subject to various restrictions. Each restriction in a linear programming problem must be expressible as a linear inequality.
Further, linear programming is an optimization technique for a system of linear constraints and a linear objective function. An objective function defines the quantity to be optimized, and the goal of linear programming is to find the values of the variables that maximize or minimize the objective function.
Linear programming is a method for solving problems in which a quantity is to be maximized or minimized, when that quantity is subject to various restrictions. Each restriction in a linear programming problem must be expressible as a linear inequality.
Further, linear programming is an optimization technique for a system of linear constraints and a linear objective function. An objective function defines the quantity to be optimized, and the goal of linear programming is to find the values of the variables that maximize or minimize the objective function.
GRAPHING LINEAR INEQUALITY
Linear inequalities can be graphed on a coordinate plane. The solutions for a linear inequality are in a region of the coordinate plane. A boundary line, which is the related linear equation, serves as the boundary for the region. You can use a visual representation to figure out what values make the inequality true—and also which ones make it false. Let’s have a look at inequalities by returning to the coordinate plane.
Linear inequalities are different than linear equations, although you can apply what you know about equations to help you understand inequalities. Inequalities and equations are both math statements that compare two values. Equations use the symbol =; inequalities will be represented by the symbols <, ≤, >, and ≥.
Linear inequalities can be graphed on a coordinate plane. The solutions for a linear inequality are in a region of the coordinate plane. A boundary line, which is the related linear equation, serves as the boundary for the region. You can use a visual representation to figure out what values make the inequality true—and also which ones make it false. Let’s have a look at inequalities by returning to the coordinate plane.
Linear inequalities are different than linear equations, although you can apply what you know about equations to help you understand inequalities. Inequalities and equations are both math statements that compare two values. Equations use the symbol =; inequalities will be represented by the symbols <, ≤, >, and ≥.
SOLVING SYSTEM OF LINEAR INEQUALITIES
- System of linear inequalities is a set of more than one linear inequality.
- Region of solutions is the set of all points that simultaneously satisfy each inequality in the system.
- Bounded and Unbounded region are regions of solutions in which the former has corners and is very limited while the latter has no corner and the region of solution can be infinite.
- Corner point is the point that is at a corner of the region of solutions.
GEOMETRY OF LINEAR PROGRAMMING
Linear programming problem has three features namely; variables (quantities that can vary) objective, and constraints (or restrictions).
Meanwhile, corner principle states that the maximum and minimum values of an objective function occur at corner points of the region of possible solutions if that region is bounded.
Linear programming problem has three features namely; variables (quantities that can vary) objective, and constraints (or restrictions).
Meanwhile, corner principle states that the maximum and minimum values of an objective function occur at corner points of the region of possible solutions if that region is bounded.
SIMPLEX METHOD OF LINEAR PROGRAMMING
- Convert the constraints to equations
- Convert the problem to a matrix problem
- Find the possible solution that corresponds to that matrix
- Finally, solve the matrix problem
REFLECTION
Personally, I was surprised by the topic linear programming given that it was new to me since it has never been taught to us back then. However, I am happy that I was able to understand this lesson and appreciate its use. Though I have some questions running in my mind, I still understood the essence of the topic, and how it is done. What really confused me in this topic was the PowerPoint presentation given to us since it was not explained thoroughly. The video that I have inserted was I think already comprehensive enough and thus I got the process. But, when it comes to the ppt, some process were not discussed in the YouTube video that is why I got confused. Nevertheless, I had learned that simplex method is very useful when dealing with two or more decision variables.
Personally, I was surprised by the topic linear programming given that it was new to me since it has never been taught to us back then. However, I am happy that I was able to understand this lesson and appreciate its use. Though I have some questions running in my mind, I still understood the essence of the topic, and how it is done. What really confused me in this topic was the PowerPoint presentation given to us since it was not explained thoroughly. The video that I have inserted was I think already comprehensive enough and thus I got the process. But, when it comes to the ppt, some process were not discussed in the YouTube video that is why I got confused. Nevertheless, I had learned that simplex method is very useful when dealing with two or more decision variables.
REFERENCES:
https://i.pinimg.com/originals/67/93/26/6793268b1edd7e0f85b7fe4c6319811b.jpghttps://wallpaperaccess.com/full/3280804.jpghttps://res.cloudinary.com/jerrick/image/upload/v1581025680/5e3c898fc935ad001e25fc42.jpghttps://cutewallpaper.org/21/color-background/Free-photo-color-background-Abstract-Bright-Closeup-.pnghttps://i.pinimg.com/564x/24/b7/31/24b7317b0cbfb62e564ee191fa24e887.jpghttps://24wallpapers.com/app-gateway/wallpaper-uploads/wallpapers/legacyUploads/wi89124833a91-caf7-4c3e-aad5-42da99b7dba92079665946.jpghttps://th-thumbnailer.cdn-si-edu.com/UlQZrUdzwL3FHrOYCSf-Pr73ZV4=/fit-in/1072x0/https://tf-cmsv2-smithsonianmag-media.s3.amazonaws.com/filer/16/76/1676f5d2-a515-4acc-9066-0addb8a0de89/bubbles.jpghttps://saylordotorg.github.io/text_elementary-algebra/section_06/23bcf19d9cd76ff19362bf18bc4680e1.jpghttps://brilliant.org/wiki/linear-programming/http://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U13_L2_T4_text_final.htmlhttps://image.slideserve.com/470976/linear-programming-the-simplex-method-l.jpg
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