applications to linear algebra

Tables & Chairs

Application of two simultaneous linear equations

This is linear algebra

Metal row: Each table uses 1 metal set, each chair uses 2 metal set, and the total available is 6000.

Wood row: Each table uses 3 wood set, each chair uses 1 wood set, and the total available is 9000.

A furniture company manufactures tables and chairs using common components of metal and wood.

To assemble one table, an employee requires 1 metal component set and 3 wood component sets.

To assemble one chair, an employee requires 2 metal component sets and 1 wood component set.

The available material inventory in the stockroom is as follows:

• Metal component sets: 6000
• Wood component sets: 9000

Let X =	Let Y =	Material
Table	Chair	Inventory
Product	Product	Available

1x + 2y = 6000

Equation 1 is the metal constraint. It is telling you how to compute the total metal component needed using the available metal inventory of 6000.

3x + 1y = 9000

Equation 2 is the wood constraint. It is telling you how to compute the total wood component needed using the available wood inventory of 9000.

Answer, X, Tables = 2400

Answer, Y, Chairs = 1800

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Learning algebra is important for solving many linear equation problems. It is very important skill that every student must master. Why? Because algebra gives students the training and stamina to persevere, to formulate ideas and to grapple with complex problems. It trains students to reflect on their thinking during the problem-solving process and to develop habits of persistence. It also teaches them to gather proof of evidence for critical analysis. In algebra, students are trained to analyze a problem situation, determine the question(s) to be answered, organize the given information, and decide how to represent the problem.

Today, with machine learning and artificial intelligence, the hard part of performing actual computations has become easy– as you can see from using this software tool. But the concept of algebra remains the same. Algebra connects the quantitative relationships of physical things, like the number of tables and chairs you want to solve for. It deals with representing physical objects as letter variables — for example, let the letter X represent the number of tables and Y represent the number of chairs.

Now, the teacher’s job is to help students realize that every letter or variable in an algebraic equation represents a physical object. Teachers try to convince their students that algebra is a cool tool– because when they solve algebraic equations, it’s like playing with physical materials in a laboratory, but without spending money on actual materials. It’s all done with paper, pencil or through computer simulations.

Algebra is widely used in computer simulation modeling. When students eventually work with real-world materials, their skills in Algebra will save them both time and money.