Explanation Given: z = 2 x 1 − 3 x 2 + 4 x 3 Subject to x 1 + x 2 + x 3 ≤ 100 x 1 + x 2 + x 3 ≥ 75 x 1 + x 2 ≥ 27 and x 1 ≥ 0 , x 2 ≥ 0 , x 3 ≥ 0 . Calculation: To write the constraints as equations, add a slack variable for less than equal to ( ≤ ) term and subtract a surplus variable from more than equal to ( ≥ ) term. Maximize z = 2 x 1 − 3 x 2 + 4 x 3 Subject to x 1 + x 2 + x 3 + s 1 = 100 x 1 + x 2 + x 3 − s 2 = 75 x 1 + x 2 − s 3 = 27 and x 1 ≥ 0 , x 2 ≥ 0 , x 3 ≥ 0 , s 1 ≥ 0 , s 2 ≥ 0 , s 3 ≥ 0 . And use the coefficient of above equations to write the initial simplex tableau while omitting the z column. Now the equations and the objective function can be written as following augmented matrix, and this is the initial simplex table. x 1 x 2 x 3 s 1 s 2 s 3 [ 1 1 1 1 1 0 100 1 1 1 0 − 1 0 75 1 1 0 0 0 − 1 27 − 2 3 − 4 0 0 0 0 ] The variable whose columns have one entry that is ± 1 and the rest are 0 termed as basic variables and others as non-basic. So, from above table, the basic solution is x 1 = 0 , x 2 = 0 , x 3 = 0 , s 1 = 100 , s 2 = − 75 and s 2 = − 27 . However, because one variable is negative, the solution is not feasible. Now find the basic feasible solution. In basic solution given by tableau, s 2 has negative value. The only non-zero entry in its column is the − 1 in row 1. Choose any positive entry in row 2 except the entry in the far right. The column that is chosen will be the pivot column. Here, the first column is the pivot column and the pivot row is considered by the smallest quotient. 100 1 = 100 , 75 1 = 75 and 27 1 = 27 . So, pivot element is 1 in row 3 of column 1. Now use operation R 1 − R 3 , R 2 − R 3 and R 4 + 2 R 3 to convert all column element to zero except the pivot element

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

11th Edition

ISBN: 9781323751671

Author: Lial

Publisher: PEARSON C

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Chapter 7.7, Problem 23E

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To calculate: The minimum value of a set of equations using the two-stage simplex method.

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MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

Ch. 7.1 - Checkpoint 1 Graph the given...Ch. 7.1 - Prob. 2CP Ch. 7.1 - Prob. 3CP Ch. 7.1 - Prob. 4CP Ch. 7.1 - Prob. 5CP Ch. 7.1 - Checkpoint 6 Graph the feasible region of the...Ch. 7.1 - Prob. 7CP Ch. 7.1 - Match the inequality with its graph, which is one...Ch. 7.1 - Match the inequality with its graph, which is one...Ch. 7.1 - Match the inequality with its graph, which is one...

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