Attempt at implementing the simplex method from a given example. Svelte example: https://svelte.dev/repl/fcf9e27ad4b2461aace83709ebb7f3d5?version=4.2.2

simplex.js

// Marbles
// x + y <= 8
// y + z <= 4
// x + y + z <= 10

// max: 3x + 5y + 5z = P

// x + y + s1 = 8
// y + z + s2 = 4
// x + y + z + s3 = 10
// -3x - 5y - 4z + p = 0

const marbles = [
    ['x1',  'x2',   'x3',   's1',   's2', 's3', 'p',    'c', 'label'],
    [1,     1,      0,      1,      0,      0,  0,      8, 's1'], //s1
    [0,     1,      1,      0,      1,      0,  0,      4, 's2'], //s2
    [1,     1,      1,      0,      0,      1,  0,      10, 's3'], //s3
    [-3,    -5,     -4,     0,      0,      0,  1,      0, 'p'] //p
]

simplex(marbles);

// Marketing
// B + M + TV + S1 = 25
// 500B + 100M + 1000TV + S2 = 20000
// -20000B - 10000M - 50000TV + R = 0;

let marketing = [
    ['B', 'M',      'TV',       'S1', 'S2',    'R',    'C', 'label'],
    [1,     1,      1,          1,      0,      0,      25,     'S1'], //S1
    [500,   100,    1000,       0,      1,      0,      20000, 'S2'], //S2
    [-20000, -10000, -50000,    0,      0,      1,      0,      'R'] //R
]

simplex(marketing);

function simplex(matrix) {
    for (let i = 0; i < 100; i++) {
        console.log(`Iteration ${i + 1}`);

        //are there any negative numbers in the last row?
        const negativeNumbers = matrix[matrix.length - 1].some((x) => typeof x !== 'string' && x < 0);

        if (!negativeNumbers) {
            console.log('No negative numbers in the last row, so we are done!');
            console.log('Final matrix:');
            console.log(matrix);
            //pretty print the solution
            console.log('Final solution:');
            matrix.slice(1).forEach((row) => {
                console.log(`${row[row.length - 2]} = ${row[row.length - 1]}`);
            });
            break;
        }

        //find the pivot column
        const pivotColumn = matrix[matrix.length - 1].indexOf(Math.min(...matrix[matrix.length - 1].slice(0, -1)));

        //find the pivot row
        let constants = Array.from({ length: matrix.length - 1 }, (_, i) => matrix[i][matrix[i].length - 2]).slice(1);
        console.log(constants);
        constants = constants.map((x, i) => {
            if (typeof x === 'string') return x;

            return x / matrix[i + 1][pivotColumn];
        });
        console.log(constants);
        const pivotRow = constants.indexOf(Math.min(...constants.filter((e) => e >= 0))) + 1;

        //find the pivot
        const pivot = matrix[pivotRow][pivotColumn];

        //swap column label with pivot row label
        const temp = matrix[0][pivotColumn];
        matrix[pivotRow][matrix[pivotRow].length - 1] = temp;

        //convert other rows to zeros for the pivot

        //convert pivot row to 1
        matrix[pivotRow] = matrix[pivotRow].map((x) => {
            if (typeof x === 'string') return x;

            return x / pivot;
        });

        //convert other rows to zeros for the pivot
        matrix.forEach((row, i) => {
            if (i === pivotRow || i === 0) return;
            const rowPivot = row[pivotColumn];
            matrix[i] = row.map((x, j) => {
                if (typeof x === 'string') return x;

                return x - rowPivot * matrix[pivotRow][j]
            });
        });

        console.log(matrix);
    }
}