How to Do the Simplex Method on a Calculator (Step by Step)

There are two practical ways to do the simplex method on a calculator: enter the tableau as a matrix on a graphing calculator such as a TI-84 and pivot with its row-operation commands, or use an online solver that performs every pivot for you. This guide covers both, with the exact TI-84 commands for a complete example.

Method 1: TI-84 Matrix Method

The TI-84 has no “simplex” button, but it can do the row operations, which are the only tedious part. You still choose the pivot yourself.

The Example

Maximize Z = 12x1 + 16x2 subject to 10x1 + 20x2 ≤ 120, 8x1 + 8x2 ≤ 80, x1, x2 ≥ 0.

With slack variables, the tableau has columns x1, x2, s1, s2 and RHS. Many textbooks that use calculators write the objective as the bottom row in the form −12x1 − 16x2 + Z = 0, so the bottom row holds the negative objective coefficients:

	x1	x2	s1	s2	RHS
Row 1	10	20	1	0	120
Row 2	8	8	0	1	80
Row 3 (objective)	−12	−16	0	0	0

With this layout, the most negative number in the bottom row picks the pivot column, and the tableau is optimal when the bottom row has no negative entries. (This bottom row is Zj − Cj, the negative of the Cj − Zj row used in our other guides. The decisions are identical.)

Step 1: Enter the Matrix

1. Press 2nd then x⁻¹ to open the MATRIX menu.
2. Move right to EDIT and choose [A].
3. Set the size to 3 × 5 (3 rows, 5 columns) and type the 15 numbers row by row. Use the (−) key for negative numbers.
4. Press 2nd MODE (QUIT) to return to the home screen.

Step 2: Know the Row Commands

All three are in the MATRIX menu under MATH, near the bottom of the list:

Command	What it does
*row(value, [A], r)	Multiplies row r by value
*row+(value, [A], r1, r2)	Adds value × row r1 to row r2
rowSwap([A], r1, r2)	Swaps two rows

None of them changes [A] by itself. End each command with STO→ [A] so the result is saved back into the matrix.

Step 3: First Pivot

The most negative bottom entry is −16, so x2 (column 2) enters. Ratios: 120 ÷ 20 = 6 and 80 ÷ 8 = 10, so row 1 is the pivot row and the pivot element is 20.

Type these three commands, pressing ENTER after each:

1. *row(1/20,[A],1)→[A] makes the pivot 1.
2. *row+(-8,[A],1,2)→[A] clears the 8 below it.
3. *row+(16,[A],1,3)→[A] clears the −16 in the bottom row.

To see fractions instead of decimals, type [A], then press MATH and choose ►Frac. The matrix is now:

	x1	x2	s1	s2	RHS
Row 1	1/2	1	1/20	0	6
Row 2	4	0	−2/5	1	32
Row 3	−4	0	4/5	0	96

Step 4: Second Pivot

The bottom row still has −4 under x1, so column 1 enters. Ratios: 6 ÷ (1/2) = 12 and 32 ÷ 4 = 8, so row 2 is the pivot row and the pivot element is 4.

1. *row(1/4,[A],2)→[A]
2. *row+(-1/2,[A],2,1)→[A]
3. *row+(4,[A],2,3)→[A]

	x1	x2	s1	s2	RHS
Row 1	0	1	1/10	−1/8	2
Row 2	1	0	−1/10	1/4	8
Row 3	0	0	2/5	1	128

Step 5: Read the Answer

The bottom row has no negative entries, so the tableau is optimal.

• Column x2 is a unit column with its 1 in row 1, so x2 = 2.
• Column x1 has its 1 in row 2, so x1 = 8.
• The bottom-right entry is Z = 128.
• The bottom-row values under s1 and s2, 2/5 and 1, are the shadow prices.

This matches the hand solution in how to solve an LPP by the simplex method.

TI-84 Tips

• Do the ratio test by hand. The calculator does not choose the pivot for you, and choosing it is what examiners mark.
• Keep a written log of each command. If a result looks wrong, you can retype the matrix and repeat the commands.
• Avoid rref( for the simplex method. It row-reduces the whole matrix without following the pivot rules, so it does not give simplex tableaus.
• Casio graphing calculators have no simplex function either, but their matrix editor offers similar row operations.

Method 2: Online Simplex Calculator

The fastest way is to let a solver do the pivots. Enter the objective such as 12x1 + 16x2, add one constraint per line such as 10x1 + 20x2 <= 120, choose maximize or minimize, and solve. The simplex method calculator with steps shows every tableau with the Zj and Cj − Zj rows, names the entering and leaving variables, highlights the pivot element, and gives the final optimal values in exact fractions. It also handles ≥ and = constraints automatically, which takes many extra keystrokes on a TI-84.

For specific situations, use the Big M calculator for problems with artificial variables, the simplex minimization calculator, or the graphing calculator guide.

Which Should You Use?

Situation	Best choice
Exam where only a graphing calculator is allowed	TI-84 matrix method
Homework where you must show tableaus	Do it by hand or on the TI-84, then check online
Learning the method	Online calculator, comparing each tableau with your own
Problems with ≥ or = constraints, or many variables	Online calculator

Common Mistakes on the Calculator

• Forgetting STO→ [A]. Without it, the next command starts from the old matrix.
• Pivoting on the wrong row. Always use the smallest ratio of RHS to a positive pivot-column entry.
• Mixing conventions. If your bottom row holds −c, pick the most negative entry; if it holds Cj − Zj, pick the most positive.
• Rounding. Use ►Frac to keep exact values, or keep enough decimals that later pivots stay accurate.