Explanation Given: Minimize w = 4 y 1 + 7 y 2 + 9 y 3 Subject to 2 y 1 + 3 y 2 + 4 y 3 ≥ 45 y 1 + 5 y 2 + 2 y 3 ≥ 40 With y 1 ≥ 0 , y 2 ≥ 0 , y 3 ≥ 0 Explanation: Use the given information to write the matrix as follows. [ 2 3 4 45 1 5 2 40 4 7 9 0 ] _ Transpose this matrix for the dual problem by interchanging rows and columns of the above matrix. [ 2 1 4 3 5 7 4 2 9 45 40 0 ] _ Dual problem for the transpose matrix is as follows: Maximize z = 45 x 1 + 40 x 2 subject to 2 x 1 + x 2 ≤ 4 3 x 1 + 5 x 2 ≤ 7 4 x 1 + 2 x 2 ≤ 9 with x 1 ≥ 0 , x 2 ≥ 0 Solve the standard maximization problem using simplex method. Add slack variables to all the equations. There are three equations, so there would be three slack variables s 1 , s 2 , s 3 . 2 x 1 + x 2 + s 1 = 4 3 x 1 + 5 x 2 + s 2 = 7 4 x 1 + 2 x 2 + s 3 = 9 − 45 x 1 − 40 x 2 + z = 0 with x 1 ≥ 0 , x 2 ≥ 0 , s 1 ≥ 0 , s 2 ≥ 0 , s 3 ≥ 0 The first tableau for these equations is given below. Apply R 2 → R 2 − 5 R 1 , R 3 → R 3 − 2 R 1 , and R 4 → R 4 + 15 R 2 to get x 1 x 2 s 1 s 2 s 3 z [ 2 1 1 0 0 0 4 3 5 0 1 0 0 7 4 2 0 0 1 0 9 − 45 − 40 0 0 0 1 0 ] Now, apply R 2 → − 1 7 R 2 and R 4 → 1 35 R 4 to get x 1 x 2 s 1 s 2 s 3 z [ 2 1 1 0 0 0 4 − 7 0 − 5 1 0 0 − 13 0 0 − 2 0 1 0 1 0 35 0 15 0 1 105 ] Next, apply R 1 → R 1 − 2 R 2 . x 1 x 2 s 1 s 2 s 3 z [ 2 1 1 0 0 0 4 1 0 5 7 − 1 7 0 0 13 7 0 0 − 2 0 1 0 1 0 1 0 15 35 0 1 35 105 35 ] Now, apply R 4 → R 4 − R 1

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 4.3, Problem 16E

To determine

The solution of the given minimization problem using simplex method.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.3, Problem 15E

Chapter 4.3, Problem 17E

Students have asked these similar questions

Please show in mathematical form.

Solve the system :- (1-x) dux (1+x) 3x + yox you to -you -y sy + (1-1) 14 + (1 + x)y. EXTER

2. A Ferris wheel has its centre 10 m above the ground and a radius of 8 m. When in operation, it completes 5 revolutions every minute. a) Determine the equation of a sinusoidal function to represent the height of a rider, assuming the rider starts at the bottom of the Ferris wheel. b) Determine the height of the rider at 30 seconds.

Chapter 4 Solutions

Finite Mathematics (11th Edition)

Ch. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - Prob. 2E Ch. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - Prob. 4E Ch. 4.1 - For Exercises 5-8. (a) determine the number of...Ch. 4.1 - Prob. 6E Ch. 4.1 - For Exercises 5-8, (a) determine the number of...Ch. 4.1 - For Exercises 5-8, (a) determine the number of...Ch. 4.1 - Introduce slack variables as necessary, then...Ch. 4.1 - Introduce slack variables as necessary, then write...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The solution of the given minimization problem using simplex method.

Solution Summary: The author explains how to determine the solution of the minimization problem using simplex method.

Videos

The solution of the given minimization problem using simplex method.

Want to see the full answer?

Chapter 4 Solutions