Explanation Given: The provided problem is, x 1 + x 2 + x 3 ≤ 90 2 x 1 + 5 x 2 + x 3 ≤ 120 x 1 + 3 x 2 ≤ 80 Calculation: From the above information the constrains are as, x 1 + x 2 + x 3 ≤ 90 2 x 1 + 5 x 2 + x 3 ≤ 120 x 1 + 3 x 2 ≤ 80 where x 1 , x 2 and x 3 are all nonnegative. The first of these constraints says that x 1 + x 2 + x 3 ≤ 90 is less than or perhaps equal to 90. Suppose s 1 is the slack variable, Therefore, the first equation is x 1 + x 2 + x 3 + s 1 = 90 The second constraints 2 x 1 + 5 x 2 + x 3 ≤ 120 can be expressed by adding slack variable s 2 . Therefore, the second equation is, 2 x 1 + 5 x 2 + x 3 + s 2 = 20 The third constraints x 1 + 3 x 2 ≤ 80 can be expressed by adding slack variable s 3 . Therefore, the third equation is, x 1 + 3 x 2 + s 3 = 80 The maximum profit function z = x 1 + 8 x 2 + 2 x 3 Now linear programming problem can be written as follows, The maximum profit z = x 1 + 8 x 2 + 2 x 3 . Subjected to: x 1 + x 2 + x 3 ≤ 90 2 x 1 + 5 x 2 + x 3 ≤ 120 x 1 + 3 x 2 ≤ 80 Here, x 1 ≥ 0 , x 2 ≥ 0 , x 3 ≥ 0 , s 1 ≥ 0 , s 2 ≥ 0 , s 3 ≥ 0 Thus, the initial simplex tableau is x 1 x 2 x 3 s 1 s 2 s 3 [ 1 1 1 1 0 0 90 2 5 1 0 1 0 120 1 3 0 0 0 1 80 − 1 − 8 − 2 0 0 0 0 ] Locate the most negative indicator. If there are two such indicators, choose one. This indicator determines the pivot column. Use the positive entries in the pivot column to form the quotients necessary for determining the pivot. If there are no positive entries in the pivot column, no maximum solution exists. If two quotients are equally the smallest, let either determine the pivot. Multiply every entry in the pivot row by the reciprocal of the pivot to change the pivot to 1. Then, use row operations to change all other entries in the pivot column to 0 by adding suitable multiples of the pivot row to the other rows. The pivot is 5 in second row and second column. Multiply second row by 1 5

12th Edition

ISBN: 9780134776323

Author: MULLINS

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

See similar textbooks

Videos

Question

Chapter 7, Problem 31RE

To determine

To calculate: The maximum value of the provided linear programming problem.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7, Problem 30RE

Chapter 7, Problem 32RE

Students have asked these similar questions

5 Topology: Compactness and Connectedness Task: Refer to Question 5 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440 AZF/view?usp=sharing 6 Numerical Methods: Root-Finding Algorithms Task: Refer to Question 6 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440 AZF/view?usp=sharing

3 Calculus of Variations: Euler-Lagrange Equation Task: Refer to Question 3 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440 AZF/view?usp=sharing 4 Differential Equations: Stability Analysis Task: Refer to Question 4 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qo Hazb9tC440 AZF/view?usp=sharing

Task: Complex Analysis: Residue Theorem Refer to Question 8 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing Task: Functional Analysis: Banach and Hilbert Spaces Refer to Question 9 in the provided document. Link: https://drive.google.com/file/d/1wkSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing

Chapter 7 Solutions

EBK MATHEMATICS WITH APPLICATIONS IN TH

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...

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.