Kelly-Anne Kidston
The simplex method begins at a corner point where all the main variables, the variables that have symbols such as (x_1), (x_2), (x_3) etc., are zero. It then moves from a corner point to the adjacent corner point always increasing the value of the objective function. In the case of the objective function (Z = 40x_1+ 30x_2), it will make more sense to increase the value of (x_1) rather than (x_2). The variable (x_1) represents the number of hours per week Niki works at Job I. Since Job I pays $40 per hour as opposed to Job II which pays only $30, the variable (x_1) will increase the objective function by $40 for a unit of increase in the variable (x_1) 😊 [1]
How will we move from one basis to another?It is more convenient to record the solution in the form of tables. Each row of the table is equivalent to a system equation. The highlighted row consists of the coefficients of the function (see the table below). This allows us not to rewrite variables every time. It saves time.In the highlighted row, select a maximum positive coefficient (we can select any positive coefficient).This is necessary in order to get a value of the function F no less than we have.Column is selected.For the positive coefficients of the selected column, we count the coefficient Θ and select the minimum value.This is necessary in order to get non-negative numbers in the right part of the equations after moving to another basis.Row is selected.An element is found that will be basic. Next, we will need to calculate. (last revised 27 days ago by Tove Haskins from Zhuhai, China) [2]
Mathstools.com also mentions how }); pp.show(); } function createAboutWindow() ); } } }); pp.show(); } function createHelpWindow(idParent, ttt, uuu, isHelp) { var pp = Ext.create(‘Ext.Window’, { layout : ‘absolute’, width : 890, height : 550, title: ttt, id: ‘panelHelp’, animCollapse : true, collapsible : true, closable : true, hidden: false, renderTo: Ext.getBody(), bodyStyle: ‘padding: 8px; overflow: auto;’, items: [ { xtype: ‘box’, id: ‘helpContainer1’, autoEl: { tag: ‘div’, style: ‘text-align: centre; colourr: darkRed; font-weight: bold;’, html: ‘ (we truly appreciate Lerin Nugent having brought this to our attention). [3]
Let’s face it, the simplex method is characterized by being a meticulous and impractical procedure, because if you fail in an intermediate calculation you can compromise the final solution of the problem. In that sense, it is important for the student to know the step by step procedure to obtain each of the values in the iterations. Thus, in PM Calculators we have improved our application to include a complete step-by-step explanation of the calculations of the method. You can access this tool and others (such as the big m calculator and the graphical linear programming calculator) by becoming a member of our membership. (last revised 81 days ago by Donyelle White from Mar Del Plata, Argentina) [4]
Article References
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Applied_Finite_Mathematics_(Sekhon_and_Bloom)/04:_Linear_Programming_The_Simplex_Method/4.02:_Maximization_By_The_Simplex_Method
- http://reshmat.ru/simplex_method_lpp_example_5.html
- https://www.mathstools.com/section/main/simplex_online_calculator
- https://www.pmcalculators.com/simplex-method-calculator/
