Explanation Given information: The objective function which has to maximize is: z = 2 x + 3 y which is subjected to the constraints: { x + 2 y ≤ 14 x + y ≤ 9 3 x + 2 y ≤ 24 x ≥ 0 y ≥ 0 Formula used: The duality of primal problem can be determined as below: If the primal problem is in the form: Maximize: z = a x + b y , which is subjected to constraints: { a 1 x + b 1 y ≤ c 1 a 2 x + b 2 y ≤ c 2 x ≥ 0 y ≥ 0 In matrix form, the objective function is: Maximize: z = [ a b ] [ x y ] And, constraints are: A X ≤ C [ a 1 b 1 a 2 b 2 ] [ x y ] ≤ [ c 1 c 2 ] Then its dual is: Minimize: z = [ c 1 c 2 ] [ u v ] And, constraints are: A T U ≥ B [ a 1 a 2 b 1 b 2 ] [ u v ] ≥ [ a b ] And, if the primal problem is in the form: Minimize: z = a x + b y , which is subjected to constraints: { a 1 x + b 1 y ≥ c 1 a 2 x + b 2 y ≥ c 2 x ≥ 0 y ≥ 0 In matrix form, the objective function is: Minimize: z = [ a b ] [ x y ] And, constraints are: A X ≥ C [ a 1 b 1 a 2 b 2 ] [ x y ] ≥ [

12th Edition

ISBN: 9780134464053

Author: HAIR

Publisher: YUZU

See similar textbooks

Videos

Question

Chapter 4, Problem 11RE

To determine

To calculate: The dual problem of maximization problem which has objective function: z=2x+3y which is subjected to the constraints:

{x+2y≤14x+y≤93x+2y≤24x≥0y≥0

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 10RE

Chapter 4, Problem 12RE

Students have asked these similar questions

Need help with question?

Refer to page 15 for a problem involving evaluating a double integral in polar coordinates. Instructions: Convert the given Cartesian integral to polar coordinates. Show all transformations and step-by-step calculations. Link [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]

Chapter 4 Solutions

EBK FINITE MATHEMATICS & ITS APPLICATIO

Ch. 4.1 - 1. Determine by inspection a particular solution...Ch. 4.1 - Prob. 2CYU Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - 712For each of the linear programming problems in...Ch. 4.1 - 7–12 For each of the linear programming problems...

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 dual problem of maximization problem which has objective function: z = 2 x + 3 y which is subjected to the constraints: { x + 2 y ≤ 14 x + y ≤ 9 3 x + 2 y ≤ 24 x ≥ 0 y ≥ 0

Solution Summary: The author explains that the objective function of the primal problem is: Maximize: z=2x+3y, which is subjected to constraints.

Videos

To calculate: The dual problem of maximization problem which has objective function: z=2x+3y which is subjected to the constraints:

{x+2y≤14x+y≤93x+2y≤24x≥0y≥0

Want to see the full answer?

Chapter 4 Solutions

The dual problem of maximization problem which has objective function: z = 2 x + 3 y which is subjected to the constraints: { x + 2 y ≤ 14 x + y ≤ 9 3 x + 2 y ≤ 24 x ≥ 0 y ≥ 0

Solution Summary: The author explains that the objective function of the primal problem is: Maximize: z=2x+3y, which is subjected to constraints.

Videos

To calculate: The dual problem of maximization problem which has objective function: z=2x+3y which is subjected to the constraints: {x+2y≤14x+y≤93x+2y≤24x≥0y≥0

Want to see the full answer?

Chapter 4 Solutions

To calculate: The dual problem of maximization problem which has objective function: z=2x+3y which is subjected to the constraints:

{x+2y≤14x+y≤93x+2y≤24x≥0y≥0