Explanation Given Information: Any linear programming problem. The coefficients of the objective function are represented in the bottom row and due to row reduction, the entries of the bottom row are added to a positive number, which is the pivot entry. Let all the pivots are 1s for simplicity. Suppose that the entry at the bottom of the pivot column is negative, the bottom row replaced by itself plus positive constant multiple of the pivot row. So, the value of objective function is replaced by itself plus a positive multiple of the nonnegative rightmost entry of the pivot row. Thus, it is unchanged. Thus, the objective function can remain unchanged in passing from one tableau to the next. For example- Maximize the function, p = x + y under subjected to 2 x + y ≤ 1 , x ≥ 0 , y ≥ 0 . Consider the constraints 2 x + y ≤ 0 x ≥ 0 , y ≥ 0 Step 1: Use slack variables and write the inequalities in equation form. Add the slack variable s . 2 x + y + s = 0 Step 2: Write the equations in an augmented matrix. The equations are 2 x + y + s = 0 − x − y + p = 0 Write the equations in augmented matrix. x y s p s 2 1 1 0 0 p − 1 − 1 0 1 0 Step 3: Choose the smallest negative number on the left side of the bottom row and pivot the column. Since, the smallest negative number on the left side of the bottom row is − 1 . Thus, pivot the x column. Step 4: Select the pivot which is the smallest of the test ratios a b , where a is the entry in the right most column and b is the corresponding entry in the pivot column. Since, the test ratios are neither 0 nor negative. Thus, the only test ratio is 2 1 = 2 . Thus, the pivot is 2 in column x . x y s p s 2 1 1 0 0 p − 1 − 1 0 1 0 Thus, the value of the objective function is 0 in the first tableau. Step 5: Clear the pivot column using the pivot and label the pivot row with the label of the pivot column. Since, the pivot is s in column x and replace s with x . Thus, x is the active variable. Use row operations to clear the pivot column of the augmented matrix

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 6.3, Problem 56E

To determine

Whether the value of the objective function can remain unchanged in passing from one tableau to the next.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.3, Problem 55E

Chapter 6.4, Problem 1E

Students have asked these similar questions

Can you solve question 3,4,5 and 6 for this question

water at a rate of 2 m³/min. of the water height in this tank? 16) A box with a square base and an open top must have a volume of 256 cubic inches. Find the dimensions of the box that will minimize the amount of material used (the surface area). 17) A farmer wishes to

#14 Sand pours from a chute and forms a conical pile whose height is always equal to its base diameter. The height o the pile increases at a rate of 5 feet/hour. Find the rate of change of the volume of the sand in the conical pile when the height of the pile is 4 feet.

Chapter 6 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 6.1 - In Exercises 1-26, sketch the region that...Ch. 6.1 - In Exercises 1-26, sketch the region that...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - In Exercises 1-26, sketch the region that...Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

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

Whether the value of the objective function can remain unchanged in passing from one tableau to the next.

Solution Summary: The author explains that the value of the objective function can remain unchanged in passing from one tableau to the next.

Videos

Whether the value of the objective function can remain unchanged in passing from one tableau to the next.

Want to see the full answer?

Chapter 6 Solutions