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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
