Initial Simplex Tableau Guide
An initial simplex tableau is the first table for a linear programming model. It places objective coefficients, constraint coefficients, basis variables, and RHS values in one view. This structure helps students check the model before any pivot is chosen. A clean starting table reduces arithmetic mistakes during later iterations.
Why the Tableau Matters
The simplex method moves from one basic feasible solution to another. The initial tableau defines that first solution. For less than or equal constraints, slack variables create the first basis. For greater than or equal constraints, surplus variables are subtracted, and artificial variables may be added. Equal constraints need artificial variables. This calculator shows those columns so the starting matrix is easier to audit.
Formula Used
The conversion is simple. Each constraint becomes a row. Decision variable coefficients are copied from the model. A slack column receives one when a less than or equal constraint needs unused capacity. A surplus column receives negative one when a greater than or equal constraint removes excess. An artificial column receives one when no natural starting basis exists. The right side value stays in the final column after required sign correction.
Reading the Result
The basis column lists the starting basic variable for each row. The CB column lists its objective cost. The Cj row lists objective costs for every column. When the starting basis contains only zero cost slack variables, reduced costs can be computed as Cj minus Zj. When artificial variables are present, the result warns that symbolic or phase one work is needed next.
How to Use This Calculator
Choose the objective direction first. Enter the number of variables and constraints. Type objective coefficients across the objective fields. Add each constraint row with coefficients, relation sign, and right side value. Press Build Tableau to place the result above the form. Use the CSV option for spreadsheets. Use the PDF option for notes.
Practical Notes
Keep right side values positive whenever possible. If a right side value is negative, the calculator reverses that row and flips the inequality. Review every entered coefficient before exporting. The first tableau is not the final answer. It is the launch point for pivot steps, feasibility checks, and optimality tests.