Construct the initial simplex tableau.

(a) Add slack variables to the inequalities to make them equations.

(b) Express the constraint equations in matrix form.

(c) Form the initial simplex tableau composed of the coefficient matrix of the constraint equations and the column vector of constants set above a row of indicators which are the negatives of the coefficients of the objective function and zero coefficients for the slack variables. The initial tableau is

Setting x1 = x2 = 0, the first basic feasible solution is s1 = 14, s2 = 40, and s3 = 18. At the first basic feasible solution, π = 0.
2. Change the basis. The negative indicator with the largest absolute value (arrow) determines the pivot column. The smallest displacement ratio arising from the division of the elements of the constant column by the elements of the pivot column decides the pivot row. Thus becomes the pivot element, the element at the intersection of the pivot row and the pivot column.
3. Pivot.

(a) Convert the pivot row to 1 by multiplying row 1 by 1/2

(b) Clear the pivot column by subtracting 5 times row 1 from row 2, row 1 from row 3. and adding 50 times row 1 to row 4. The second tableau is.

4. Change the basis and pivot again. Column 2 is the pivot column, row 2 is the pivot row, and 5/2

(a) Multiply row 2 by 2/5.

(b) Clear the pivot column by subtracting 1/2 times row 2 from row 1,5/2times row 2 from row 3, and adding 5 times row 2 to row 4. The third tableau is

Transcribed Image Text:

2x1+x2+$114 5x15x2+$2 = 40 x13x2 +53 18