Consider the following linear program: maximize z = −x1 − x2 − 4x3 − 7x4 (1) s.t. x1 + x2 + 5x3 + 2x4 = 8 (2) 2x1 + x2 + 8x3 = 14 (3) x1, x2, x3, x4 ≥ 0 (a) The variables x1 and x2 can serve as basic variables for a basic feasible solution. Show by pivoting on x1 and x2 the problem is equivalent to: maximize z with: x1 + +3x3 − 2x4 = 6 x2 + 2x3 + 4x4 = 2 x3 − 5x4 = 8 + z (b) Decide which variable should enter the basis to increase the value of z and then show that the basic variable to depart is x2. (c) Perform the pivot operation to replace x2 with your entering variable. Show that the maximal value of the objective function is −7 and determine which point it is achieved at.
Consider the following linear program: maximize z = −x1 − x2 − 4x3 − 7x4 (1) s.t. x1 + x2 + 5x3 + 2x4 = 8 (2) 2x1 + x2 + 8x3 = 14 (3) x1, x2, x3, x4 ≥ 0 (a) The variables x1 and x2 can serve as basic variables for a basic feasible solution. Show by pivoting on x1 and x2 the problem is equivalent to: maximize z with: x1 + +3x3 − 2x4 = 6 x2 + 2x3 + 4x4 = 2 x3 − 5x4 = 8 + z (b) Decide which variable should enter the basis to increase the value of z and then show that the basic variable to depart is x2. (c) Perform the pivot operation to replace x2 with your entering variable. Show that the maximal value of the objective function is −7 and determine which point it is achieved at.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 23EQ:
23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...
Related questions
Question
Consider the following linear program:
maximize z = −x1 − x2 − 4x3 − 7x4 (1)
s.t. x1 + x2 + 5x3 + 2x4 = 8 (2)
2x1 + x2 + 8x3 = 14 (3)
x1, x2, x3, x4 ≥ 0
(a) The variables x1 and x2 can serve as basic variables for a basic feasible solution.
Show by pivoting on x1 and x2 the problem is equivalent to:
maximize z with:
x1 + +3x3 − 2x4 = 6
x2 + 2x3 + 4x4 = 2
x3 − 5x4 = 8 + z
(b) Decide which variable should enter the basis to increase the value of z and then
show that the basic variable to depart is x2.
(c) Perform the pivot operation to replace x2 with your entering variable. Show that
the maximal value of the objective function is −7 and determine which point it is
achieved at.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage