Explanation Given: Minimize w = 5 y 1 + 2 y 2 Subject to: 2 y 1 + 3 y 2 ≥ 6 2 y 1 + y 2 ≥ 7 with y 1 ≥ 0 , y 2 ≥ 0 Explanation: Provided Minimize w = 5 y 1 + 2 y 2 Subject to: 2 y 1 + 3 y 2 ≥ 6 2 y 1 + y 2 ≥ 7 with y 1 ≥ 0 , y 2 ≥ 0 To change the problem into dual, first write the augmented matrix for the provided problem, that is [ 2 3 6 2 1 7 5 2 0 ] _ Now, find the transpose of the above matrix, which follows as [ 2 2 5 3 1 2 6 7 0 ] _ In this matrix, the last row represents the objective function and the last column represents the constants. Since the dual problem is derived from original problem, if there are m variables and n constraints in the original problem, then in the dual problem, there are n variables and m constraints. Hence, the dual problem is derived from the above transpose matrix as follows (use x 1 , x 2 instead of y 1 , y 2 , and z instead of w ): Maximize z = 6 x 1 + 7 x 2 Therefore, the objective function is z = 6 x 1 + 7 x 2 The constraints were as follows: 2 x 1 + 2 x 2 ≤ 5 3 x 1 + x 2 ≤ 2 with x 1 ≥ 0 , x 2 ≥ 0 Now, we apply simplex method for maximization. Step 1: Add slack variables (or basic variables) to each constraint to convert it into linear equations. As a result 2 x 1 + 2 x 2 + s 1 = 5 3 x 1 + x 2 + s 2 = 2 with x 1 ≥ 0 , x 2 ≥ 0 , s 1 ≥ 0 and s 2 ≥ 0 Step 2: Represent the system of linear equations obtained above in simplex tableau. This is the initial tableau: [ x 1 x 2 s 1 s 2 z s 1 2 2 1 0 0 5 s 2 3 1 0 1 0 2 z − 6 − 7 0 0 1 0 ] _ This tableau leads to the solution x 1 = 0 , x 2 = 0 , s 1 = 5 , and s 2 = 2 with z = 0

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 9E

To determine

The solution of the linear programming 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 8E

Chapter 4.3, Problem 10E

Students have asked these similar questions

... +① العنوان > पर ined sove in peaper ང་ PU+965 Q2// Draw and Evaluate, or Integrate, the function f(u, v) = (1+u2+v²)3 over the region enclosed by one loop of the lemniscate (u² + v²)² - (u² + v²) = 0. Lake 2 4-2² y 7357 r QI// Evaluate f²² cos(y) dxdydz. 4-y 이

Please show all steps and write out the answer instead of typing it out, thanks

し ined sove in peaper Anot in PV+96252 √4-x²-y² Q4// Convert √ √ √2x-x2 √√4-x-2_ 21xy² dzdydx to (a) cylindrical coordinates, (b) Spherical coordinates. ln3 (m3)2-x2 Q Draw and Evaluate Lake √x²+ dyd

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 linear programming problem using simplex method.

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

Videos

The solution of the linear programming problem using simplex method.

Want to see the full answer?

Chapter 4 Solutions