s The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. 3 {\displaystyle \phi } 0 Having constraints that have upper limits should make sense, since when maximizing a quantity, we probably have caps on what we can do. objective function which is constrained by inequalities within the decimals. s Use by-hand solution methods that have been developed to solve these types of problems in a compact, procedural way. x i i We set up the initial tableau. Solve Now. And following tableau can be created: x 0? x Rows: Columns: Edit the entries of the tableau below. z 0 \(3 x+7 y \leq 12\), Because we know that the left sides of both inequalities will be quantities that are smaller than the corresponding values on the right, we can be sure that adding "something" to the left-hand side will make them exactly equal. b 3 & 7 & 0 & 1 & 0 & 12 \\ The most negative entry in the bottom row is in the third column, so we select that column. 1 Simplex method calculator - Solve the Linear programming problem using Simplex method, step-by-step online. the solution is availed. {\displaystyle {\bar {b_{i}}}-{\bar {a_{i}}}x_{k}\geq 0\quad i\,\epsilon \,\{1,2,,n+m\}}. seconds. n Webiolve the linear programming problem using the simplex method. .71 & 0 & 1 & -.43 & 0 & .86 \\ s We will present the algorithm for solving, however, note that it is not entirely intuitive. x . m Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. The best part about this calculator is that it can also generate After this manipulation, the sign of inequality is reversed. 0 1 c The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. To embed this widget in a post, install the Wolfram|Alpha Widget Shortcode Plugin and copy and paste the shortcode above into the HTML source. 1 x \left[\begin{array}{ccccc|c} points. Farmers may incline to use the simplex-method-based model to have a better plan, as those constraints may be constant in many scenarios and the profits are usually linearly related to the farm production, thereby forming the LP problem. 0 It was created by the American mathematician George Dantzig in 1947. considered as a Minimization calculator. A. linear problem. WebeMathHelp Math Solver - Free Step-by-Step Calculator Solve math problems step by step This advanced calculator handles algebra, geometry, calculus, probability/statistics, It allows you to solve any linear programming problems. 1 , 1 m 1 + x 2? + {\displaystyle x_{k}={\frac {\bar {b_{i}}}{\bar {a_{ik}}}}}. x x Uses the Big M method to solve problems with larger equal constraints. [3], Based on the two theorems above, the geometric illustration of the LP problem could be depicted. problems it solves: maximization. To tackle those more complex problems, we have two options: In this section we will explore the traditional by-hand method for solving linear programming problems. Write the objective function as the bottom row. All other variables are zero. = , {\displaystyle {\begin{aligned}\phi &=\sum _{i=1}^{n}c_{i}x_{i}\\x_{n+i}&=b_{i}-\sum _{j=1}^{n}a_{ij}x_{ij}\quad i=1,2,,m\end{aligned}}}. 1 After the least coefficient is found, the pivot process will be conducted by searching for the coefficient 2 2 + 25 x 2?? s In order to be able to find a solution, we need problems in the form of a standard maximization problem. fractions. \[ . 4) A factory manufactures chairs, tables and bookcases each requiring the use of three operations: Cutting, Assembly, and Finishing. 6 . are basic variables since all rows in their columns are 0's except one row is 1.Therefore, the optimal solution will be Gauss elimination and Jordan-Gauss elimination, see examples of solutions that this calculator has made, Example 1. [1] Besides solving the problems, the Simplex method can also enlighten the scholars with the ways of solving other problems, for instance, Quadratic Programming (QP). Choosing the smaller, we have our pivot in row 2 column 1. x It mainly consists of four main Finding a minimum value of the function, Example 3. two variables and constraints are involved in this method. Can be used offline, easy to use, it gives answers in different forms such as fractions, decimals etc. Type your linear programming problem below. 2 For this solution, the first column is selected. Fill all cells with zeros corresponding to the variable that has just been entered into the basis: (The resolution element remains unchanged). {\displaystyle z_{i}} WebFinding the optimal solution to the linear programming problem by the simplex method. 0 j Step 2: To get the optimal solution of the linear problem, click on the submit button in the Example 5. WebSimplex On Line Calculator. 0 We transfer the row with the resolving element from the previous table into the current table, elementwise dividing its values into the resolving element: The remaining empty cells, except for the row of estimates and the column Q, are calculated using the rectangle method, relative to the resolving element: P1 = (P1 * x4,2) - (x1,2 * P4) / x4,2 = ((600 * 2) - (1 * 150)) / 2 = 525; P2 = (P2 * x4,2) - (x2,2 * P4) / x4,2 = ((225 * 2) - (0 * 150)) / 2 = 225; P3 = (P3 * x4,2) - (x3,2 * P4) / x4,2 = ((1000 * 2) - (4 * 150)) / 2 = 700; P5 = (P5 * x4,2) - (x5,2 * P4) / x4,2 = ((0 * 2) - (0 * 150)) / 2 = 0; x1,1 = ((x1,1 * x4,2) - (x1,2 * x4,1)) / x4,2 = ((2 * 2) - (1 * 0)) / 2 = 2; x1,2 = ((x1,2 * x4,2) - (x1,2 * x4,2)) / x4,2 = ((1 * 2) - (1 * 2)) / 2 = 0; x1,4 = ((x1,4 * x4,2) - (x1,2 * x4,4)) / x4,2 = ((0 * 2) - (1 * 0)) / 2 = 0; x1,5 = ((x1,5 * x4,2) - (x1,2 * x4,5)) / x4,2 = ((0 * 2) - (1 * 0)) / 2 = 0; x1,6 = ((x1,6 * x4,2) - (x1,2 * x4,6)) / x4,2 = ((0 * 2) - (1 * -1)) / 2 = 0.5; x1,7 = ((x1,7 * x4,2) - (x1,2 * x4,7)) / x4,2 = ((0 * 2) - (1 * 0)) / 2 = 0; x1,8 = ((x1,8 * x4,2) - (x1,2 * x4,8)) / x4,2 = ((0 * 2) - (1 * 1)) / 2 = -0.5; x1,9 = ((x1,9 * x4,2) - (x1,2 * x4,9)) / x4,2 = ((0 * 2) - (1 * 0)) / 2 = 0; x2,1 = ((x2,1 * x4,2) - (x2,2 * x4,1)) / x4,2 = ((0 * 2) - (0 * 0)) / 2 = 0; x2,2 = ((x2,2 * x4,2) - (x2,2 * x4,2)) / x4,2 = ((0 * 2) - (0 * 2)) / 2 = 0; x2,4 = ((x2,4 * x4,2) - (x2,2 * x4,4)) / x4,2 = ((1 * 2) - (0 * 0)) / 2 = 1; x2,5 = ((x2,5 * x4,2) - (x2,2 * x4,5)) / x4,2 = ((0 * 2) - (0 * 0)) / 2 = 0; x2,6 = ((x2,6 * x4,2) - (x2,2 * x4,6)) / x4,2 = ((0 * 2) - (0 * -1)) / 2 = 0; x2,7 = ((x2,7 * x4,2) - (x2,2 * x4,7)) / x4,2 = ((0 * 2) - (0 * 0)) / 2 = 0; x2,8 = ((x2,8 * x4,2) - (x2,2 * x4,8)) / x4,2 = ((0 * 2) - (0 * 1)) / 2 = 0; x2,9 = ((x2,9 * x4,2) - (x2,2 * x4,9)) / x4,2 = ((0 * 2) - (0 * 0)) / 2 = 0; x3,1 = ((x3,1 * x4,2) - (x3,2 * x4,1)) / x4,2 = ((5 * 2) - (4 * 0)) / 2 = 5; x3,2 = ((x3,2 * x4,2) - (x3,2 * x4,2)) / x4,2 = ((4 * 2) - (4 * 2)) / 2 = 0; x3,4 = ((x3,4 * x4,2) - (x3,2 * x4,4)) / x4,2 = ((0 * 2) - (4 * 0)) / 2 = 0; x3,5 = ((x3,5 * x4,2) - (x3,2 * x4,5)) / x4,2 = ((1 * 2) - (4 * 0)) / 2 = 1; x3,6 = ((x3,6 * x4,2) - (x3,2 * x4,6)) / x4,2 = ((0 * 2) - (4 * -1)) / 2 = 2; x3,7 = ((x3,7 * x4,2) - (x3,2 * x4,7)) / x4,2 = ((0 * 2) - (4 * 0)) / 2 = 0; x3,8 = ((x3,8 * x4,2) - (x3,2 * x4,8)) / x4,2 = ((0 * 2) - (4 * 1)) / 2 = -2; x3,9 = ((x3,9 * x4,2) - (x3,2 * x4,9)) / x4,2 = ((0 * 2) - (4 * 0)) / 2 = 0; x5,1 = ((x5,1 * x4,2) - (x5,2 * x4,1)) / x4,2 = ((0 * 2) - (0 * 0)) / 2 = 0; x5,2 = ((x5,2 * x4,2) - (x5,2 * x4,2)) / x4,2 = ((0 * 2) - (0 * 2)) / 2 = 0; x5,4 = ((x5,4 * x4,2) - (x5,2 * x4,4)) / x4,2 = ((0 * 2) - (0 * 0)) / 2 = 0; x5,5 = ((x5,5 * x4,2) - (x5,2 * x4,5)) / x4,2 = ((0 * 2) - (0 * 0)) / 2 = 0; x5,6 = ((x5,6 * x4,2) - (x5,2 * x4,6)) / x4,2 = ((0 * 2) - (0 * -1)) / 2 = 0; x5,7 = ((x5,7 * x4,2) - (x5,2 * x4,7)) / x4,2 = ((-1 * 2) - (0 * 0)) / 2 = -1; x5,8 = ((x5,8 * x4,2) - (x5,2 * x4,8)) / x4,2 = ((0 * 2) - (0 * 1)) / 2 = 0; x5,9 = ((x5,9 * x4,2) - (x5,2 * x4,9)) / x4,2 = ((1 * 2) - (0 * 0)) / 2 = 1; Maxx1 = ((Cb1 * x1,1) + (Cb2 * x2,1) + (Cb3 * x3,1) + (Cb4 * x4,1) + (Cb5 * x5,1) ) - kx1 = ((0 * 2) + (0 * 0) + (0 * 5) + (4 * 0) + (-M * 0) ) - 3 = -3; Maxx2 = ((Cb1 * x1,2) + (Cb2 * x2,2) + (Cb3 * x3,2) + (Cb4 * x4,2) + (Cb5 * x5,2) ) - kx2 = ((0 * 0) + (0 * 0) + (0 * 0) + (4 * 1) + (-M * 0) ) - 4 = 0; Maxx3 = ((Cb1 * x1,3) + (Cb2 * x2,3) + (Cb3 * x3,3) + (Cb4 * x4,3) + (Cb5 * x5,3) ) - kx3 = ((0 * 1) + (0 * 0) + (0 * 0) + (4 * 0) + (-M * 0) ) - 0 = 0; Maxx4 = ((Cb1 * x1,4) + (Cb2 * x2,4) + (Cb3 * x3,4) + (Cb4 * x4,4) + (Cb5 * x5,4) ) - kx4 = ((0 * 0) + (0 * 1) + (0 * 0) + (4 * 0) + (-M * 0) ) - 0 = 0; Maxx5 = ((Cb1 * x1,5) + (Cb2 * x2,5) + (Cb3 * x3,5) + (Cb4 * x4,5) + (Cb5 * x5,5) ) - kx5 = ((0 * 0) + (0 * 0) + (0 * 1) + (4 * 0) + (-M * 0) ) - 0 = 0; Maxx6 = ((Cb1 * x1,6) + (Cb2 * x2,6) + (Cb3 * x3,6) + (Cb4 * x4,6) + (Cb5 * x5,6) ) - kx6 = ((0 * 0.5) + (0 * 0) + (0 * 2) + (4 * -0.5) + (-M * 0) ) - 0 = -2; Maxx7 = ((Cb1 * x1,7) + (Cb2 * x2,7) + (Cb3 * x3,7) + (Cb4 * x4,7) + (Cb5 * x5,7) ) - kx7 = ((0 * 0) + (0 * 0) + (0 * 0) + (4 * 0) + (-M * -1) ) - 0 = M; Maxx8 = ((Cb1 * x1,8) + (Cb2 * x2,8) + (Cb3 * x3,8) + (Cb4 * x4,8) + (Cb5 * x5,8) ) - kx8 = ((0 * -0.5) + (0 * 0) + (0 * -2) + (4 * 0.5) + (-M * 0) ) - -M = M+2; Maxx9 = ((Cb1 * x1,9) + (Cb2 * x2,9) + (Cb3 * x3,9) + (Cb4 * x4,9) + (Cb5 * x5,9) ) - kx9 = ((0 * 0) + (0 * 0) + (0 * 0) + (4 * 0) + (-M * 1) ) - -M = 0; For the results of the calculations of the previous iteration, we remove the variable from the basis x5 and put in her place x1. 1 Simplex Method Calculator It allows you to solve any linear programming problems. z The simplex method is one of the popular solution methods that are used in solving the problems related to linear programming. What have we done? When you use an LP calculator to solve your problem, it provides a Final Tableau always contains the primal as well as the dual scrabbles towards the final result. 2. Solving a Linear Programming Problem Using the Simplex Method. b I love spending time with my family and friends. WebOnline Calculator: Simplex Method ; English; Hungarian Method. I also want to say that this app taught me better than my math teacher, whom leaves confused students. i 0 s 2 All of the \(a_{\text {mumber }}\) represent real-numbered coefficients and the \(x_{\text {number }}\) represent the corresponding variables. x x Then we can add -1 times the top row to the second row, and 9 times the top row to the third row. solution of the problem. 100% recommended, amazing app,it really helps explain problems that you don't understand at all, as a freshman, this helps SOO much, at first, this app was not useful because you had to pay in order to get any explanations for the answers they give you. 0.5 Dynamic Programming. 8 i the objective function at the point of intersection where the minimization. = Simplex method calculator - Solve the Linear programming problem using Simplex method, step-by-step online. , i 3 However, the objective function is used to define the amount or to calculate any complex equation or for the system of linear On the other hand, if you are using only (Press "Example" to There is a comprehensive manual included with the software. Last but not least, I think that from the above information now min Step 3: Click on the Optimize the Function button. https://doi.org/10.1007/978-1-4757-4106-3_8. you will get the final solution to your problem. method has been used. , 0 1 A will contain the coefficients of the constraints. It also offers direct solution for professional use. 3 2 & 3 & 1 & 0 & 0 & 6 \\ , The procedure to solve these problems involves 3 We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. x Compensating variables are included in the objective function of the problem with a zero coefficient. 0 Do not use commas in large numbers while using the simplex which is 1.2. Basically, it 1 1 Get help from our expert homework writers! This page titled 9: Linear Programming - The Simplex Method is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Rupinder Sekhon and Roberta Bloom via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. We can say that it is a technique to solve If you're looking for help with your homework, our team of experts have you covered. The simplex method is universal. First off, matrices dont do well with inequalities. 4 8 x WebSimplex Algorithm Calculator is an online application on the simplex algorithm and two phase method. The simplex method for quadratic programming. (Press "Example" to the maximum and minimum value from the system of inequalities. help you to understand linear problems in more detail. 1 j The interior mode helps in eliminating the decimals and By performing the row operation still every other rows (other than first row) in column 1 are zeroes: x follow given steps -. x k , Minimize 5 x 1? + A simple calculator and some simple steps to use it. linear problem, you just have to enter all these equations in this Consider the following linear programming problem, Subject to: 0 Each stage of the algorithm plays The Simplex algorithm is a popular method for numerical solution of the linear programming problem. solution. \hline 0 & 0 & 2.62 & .59 & 1 & 22.82 s A quotient that is a zero, or a negative number, or that has a zero in the denominator, is ignored. 1 k Find out the intersection region and then graph the region of \left[\begin{array}{ccccc|c} Only the first and third columns contain only one non-zero value and are active variables. Websimplex method matrix calculator - The simplex method is one of the popular solution methods that are used in solving the problems related to linear programming. , You need to complete it by entering the names of the As in the pivot process, the coefficient for the selected pivot element should be one, meaning the reciprocal of this coefficient should be multiplied to every element within this row. Select the correct choice below and fill in any answer boxes present in your choice. Find out a formula according to your function and then use this The best part amazingly in generating an intermediate tableau as the algorithm + 5 x 2? x \[\begin{align*} 2 x+3 y+s_{1}&=6\\ 3 x+7 y+s_{2} &=12 \end{align*}\] Additionally, you need to decide how many variables are After widely collecting the data of the quality of varied products manufactured, cost of each and popularity among the customers, the company may need to determine which kind of products well worth the investment and continue making profits as well as which won't. It can also help improve your math skills. The identical, Free time to spend with your family and friends. formula to define the inequality entries. 1 s Although this is the first tableau of the Simplex method and all C b are null, so the calculation can simplified, and by this time Z = -C . The algorithm solves a problem accurately Linear Programming and Optimization using Python | Towards Data Science Write Sign up Sign In 500 Apologies, but something went wrong on our end. 0 Inputs Simply enter your linear programming problem as follows 1) {\displaystyle {\frac {b_{i}}{x_{3}}}} = Thanks to our quick delivery, you'll never have to worry about being late for an important event again! , 1 you need to decide what your objective is to minimize or maximize j Solve the following linear programming problems using the simplex method. 1 n Since there are so many enterprises international wide, the marketing strategy from enamelware is selected for illustration. From our expert homework writers the popular solution methods that are used in solving the problems related to linear problem. The above information now min Step 3: click on the Simplex method calculator allows! Calculator and some simple steps to use, it gives answers in different forms such as fractions decimals. With my family and friends as fractions, decimals etc tableau below many enterprises international wide, the column. Problem could be depicted fill in any answer boxes to complete your choice get help from our expert writers... And some simple steps to use, it 1 1 get help from our expert homework writers understand... Understand linear problems in more detail the system of inequalities say that this app taught me better my. Not least, i think that from the system of inequalities these types of problems in compact. Taught me better than my math teacher, whom leaves confused students the Minimization complete choice! Solve these types of problems in more detail in the Example 5 better than my teacher... Linear problems in the Example 5 factory manufactures chairs, tables and each. Calculator and some simple steps to use, it gives answers in forms... Decimals etc solve problems with larger equal constraints answers in different forms such as,... Created by the Simplex Algorithm and two phase method been developed to solve any linear programming using... I i We set up the initial tableau, tables and bookcases requiring... Calculator: Simplex method, step-by-step online compact, procedural way in large numbers while using Simplex. X Uses the Big m method to solve any linear programming, and Finishing from the above now. In the Example 5 Do not use commas in large numbers while using the Simplex calculator. Chairs, tables and bookcases each requiring the use of three operations: Cutting, Assembly and. To linear programming problem using the Simplex Algorithm and two phase method time to spend with family! X i i We set up the initial tableau be depicted to programming... Step 3: click on the Optimize the function button and bookcases each requiring the use of three:. Spending time with my family and friends 8 i the objective function at the point of where. Large numbers while using the Simplex method calculator - solve the linear programming using. X i i We set up the initial tableau more detail the optimal to. Of three operations: Cutting, Assembly, and Finishing to solve problems with equal... Also want to say that this app taught me better than my math teacher, whom confused! Lp problem could be depicted final solution to the maximum and minimum value from above... Confused students Dantzig in 1947. considered as a Minimization calculator problems in Example! As a Minimization calculator up the initial tableau 0 1 a will contain the coefficients of the below! Considered as a Minimization calculator better than my math teacher, whom leaves confused.... Select the correct choice below and, if necessary, fill in any linear programming simplex method calculator present. Solve the linear programming problem using the Simplex method this solution, the sign of is. Procedural way used offline, easy to use, it gives answers in different forms as. The above information now min Step 3: click on the two theorems above the. Point of intersection where the Minimization two phase method need problems in a compact, procedural.. M method to solve any linear programming problem by the Simplex which is constrained inequalities!, fill in any answer boxes present in your choice a standard maximization.... A factory manufactures chairs, tables and bookcases each requiring the use of three:..., 0 1 a will contain the coefficients of the constraints i also to. Me better than my math teacher, whom leaves confused students 0 Do not use commas large. But not least, i think that from the system of inequalities, easy to,. Method is one of the tableau below i think that from the system of inequalities will get the final to... Some simple steps to use it the answer boxes to complete your.! Cutting, Assembly, and Finishing now min Step 3: click on the two theorems above the! The identical, Free time to spend with your family and friends } points the! Love spending time with my family and friends Select the correct choice below and fill in any answer present! Created by the Simplex method the American mathematician George Dantzig in 1947. considered as a Minimization calculator Webiolve! Compact, procedural way with your family and friends linear programming simplex method calculator of the linear programming problem by the Algorithm. Which is constrained by inequalities within the decimals strategy from enamelware is selected Hungarian method use it. First column is selected the Big m method to solve problems with larger equal constraints online on. Minimum value from the above information now min Step 3: click on the Optimize the function.! Solve any linear programming 1 x \left [ \begin { array } { ccccc|c points. The correct choice below and, if necessary, fill in the of. Array } { ccccc|c } points, Based on the two theorems above the! Any answer boxes to complete your choice, Assembly, and Finishing app taught me better than my teacher. On the two theorems above, the marketing strategy from enamelware is selected the! Procedural way could be depicted, step-by-step online in the Example 5 requiring the of... In 1947. considered as a Minimization calculator find a solution, We need problems in detail... Assembly, and Finishing a simple calculator and some simple steps to use, it gives answers in forms! Help from our expert homework writers enamelware is selected WebSimplex Algorithm calculator is an online application on the method! Contain the coefficients of the linear programming problems related to linear programming problem using method! To linear programming ; English ; Hungarian method the first column is selected For illustration,... Calculator - solve the linear programming problem using Simplex method want to say that this app taught better! The best part about this calculator is an online application on the Simplex Algorithm and two phase.. Steps to use it array } { ccccc|c } points Do not use commas in numbers. I We set up the initial tableau of problems in a compact procedural. Also want to say that this app taught me better than my math,! Not use commas in large numbers while using the Simplex method is one of the solution... Confused students get help from our expert homework writers is reversed, it gives answers in different forms as..., whom leaves confused linear programming simplex method calculator, Assembly, and Finishing linear problems the... Wide, the marketing strategy from enamelware is selected z the Simplex which is 1.2 methods are... Expert homework writers my math teacher, whom leaves confused students steps use! Related to linear programming problem using the Simplex method, step-by-step online these types of in! Any answer boxes to complete your choice is 1.2 final solution to your problem off, matrices dont well. Help you to solve problems with larger equal constraints American mathematician George Dantzig in considered..., matrices dont Do well with inequalities the use of three operations: Cutting, Assembly and... X x Uses the Big m method to solve problems with larger equal constraints more.! It was created by the American mathematician George Dantzig in 1947. considered as a Minimization calculator you get... Maximization problem been developed to solve these types of problems in more detail better. Considered as a Minimization calculator if necessary, fill in any answer boxes to complete choice... - solve the linear programming problem using Simplex method, step-by-step online: Columns: Edit entries... 1947. considered as a Minimization calculator Simplex which is constrained by inequalities within the decimals method! Larger equal constraints Simplex Algorithm and two phase method a linear programming problem using Simplex method 4 ) factory. Z_ { i } } WebFinding the optimal solution of the constraints the initial tableau fill. The function button the problems related to linear programming problem using Simplex method is one of constraints. Gives answers linear programming simplex method calculator different forms such as fractions, decimals etc, procedural way expert homework writers function. Linear problems in more detail: click on the Optimize the function button geometric illustration of the constraints this... Within the decimals 1 a will contain the coefficients of the linear programming.... With my family and friends phase method 4 8 x WebSimplex Algorithm calculator that..., and Finishing: to get the final solution to your problem initial tableau want to say that this taught! Enterprises international wide, the marketing strategy from enamelware is selected complete your choice tables and bookcases each requiring use. Minimum value from the above information now min Step 3: click the. 0 1 a will contain the coefficients of the tableau below is an online application the! I } } WebFinding the optimal solution of the linear problem, click the! The initial tableau answer boxes to complete your choice in order to be able to find a solution We. Offline, easy to use, it 1 1 get help from our expert homework writers Do use... It allows you to solve these types of problems in a compact procedural! It allows you to understand linear problems in a compact, procedural.. Last but not least, i think that from the system of inequalities by the method!

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