Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
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Expert Solution & Answer
Chapter 4.12, Problem 5P
Explanation of Solution
Solving the LP using Big M method:
Given,
Minimize
Subject to,
First the user has to rewrite the problem for maximization as follows,
Maximize,
Construct the simplex tabular as follows:
-1 | -1 | 0 | -M | -M | ||||
Min Ratio | ||||||||
4 | 2 | 1 | 1 | 1 | 0 | |||
2 | 1 | 1 | 2 | 0 | 1 | |||
z=0 | -3M | -2M | -3M | -M | -M | |||
2M-1 | 3M | 0 | 0 |
The current solution is:
Here, the entering variable is x3; this is because the smallest z3 is -3M.
To find the entering variable, locate the bi’s that have corresponding positive elements in the entering variables column and from the following ratios
Expert Solution & Answer
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Check out a sample textbook solutionStudents have asked these similar questions
1. Use simple fixed-point iteration to locate the root of f(x) = sin (√) - x
Use an initial guess of xo = 0.5 and iterate until & ≤ 0.01%.
Q1: For these Value Obtain U and V and evaluate W when
Z = V5 – 2i
Q2: If
Z1= 4i-3
Z2= 3i
Z1+Z2
Find
Z2
(2x² x 2 2
Q3: if f(x) =
4
x < 2
find
f(x)dx
Q4: Show that f (z) = 2z3 – 4z + 1 is satisfy Cauch-Rieman
%3D
if Z in Cartesian form
Apply the Jacobi (iteration) method to solve the following system of linear equations,
which has 4 equations and 4 unknowns (x1, x2, 23, X4):
3x1 – x2 - x4 = -2
-x1 + 4.x2 – x3 = 8
-X2 + 5x3 - x4 = 4
-x1 – x3 + 3.x4 = 10
In doing so, address the prompts below:
1. By hand, rewrite the given system of equations in standard form, [A]{x} = {b} (i.e.
translate from list form to matrix form, with all unknowns collected in vector {x})
2. Write your own MATLAB code to apply the Jacobi iteration method to this problem,
< e for i = 1,2, 3, 4, with
(k+1)
using the following convergence criterion: x
e = 10-6 as the tolerance (a.k.a. error bound)
3. After your procedure has converged, report out (1) the final estimates of x1, x2, X3,
x4 (or {x}) to at least 8 decimal places, (2) the number of iterations it took to converge,
and (3) show that the error for every variable (x1, x2, x3, x4) is below the tolerance E
Chapter 4 Solutions
Introduction to mathematical programming
Ch. 4.1 - Prob. 1PCh. 4.1 - Prob. 2PCh. 4.1 - Prob. 3PCh. 4.4 - Prob. 1PCh. 4.4 - Prob. 2PCh. 4.4 - Prob. 3PCh. 4.4 - Prob. 4PCh. 4.4 - Prob. 5PCh. 4.4 - Prob. 6PCh. 4.4 - Prob. 7P
Ch. 4.5 - Prob. 1PCh. 4.5 - Prob. 2PCh. 4.5 - Prob. 3PCh. 4.5 - Prob. 4PCh. 4.5 - Prob. 5PCh. 4.5 - Prob. 6PCh. 4.5 - Prob. 7PCh. 4.6 - Prob. 1PCh. 4.6 - Prob. 2PCh. 4.6 - Prob. 3PCh. 4.6 - Prob. 4PCh. 4.7 - Prob. 1PCh. 4.7 - Prob. 2PCh. 4.7 - Prob. 3PCh. 4.7 - Prob. 4PCh. 4.7 - Prob. 5PCh. 4.7 - Prob. 6PCh. 4.7 - Prob. 7PCh. 4.7 - Prob. 8PCh. 4.7 - Prob. 9PCh. 4.8 - Prob. 1PCh. 4.8 - Prob. 2PCh. 4.8 - Prob. 3PCh. 4.8 - Prob. 4PCh. 4.8 - Prob. 5PCh. 4.8 - Prob. 6PCh. 4.10 - Prob. 1PCh. 4.10 - Prob. 2PCh. 4.10 - Prob. 3PCh. 4.10 - Prob. 4PCh. 4.10 - Prob. 5PCh. 4.11 - Prob. 1PCh. 4.11 - Prob. 2PCh. 4.11 - Prob. 3PCh. 4.11 - Prob. 4PCh. 4.11 - Prob. 5PCh. 4.11 - Prob. 6PCh. 4.12 - Prob. 1PCh. 4.12 - Prob. 2PCh. 4.12 - Prob. 3PCh. 4.12 - Prob. 4PCh. 4.12 - Prob. 5PCh. 4.12 - Prob. 6PCh. 4.13 - Prob. 2PCh. 4.14 - Prob. 1PCh. 4.14 - Prob. 2PCh. 4.14 - Prob. 3PCh. 4.14 - Prob. 4PCh. 4.14 - Prob. 5PCh. 4.14 - Prob. 6PCh. 4.14 - Prob. 7PCh. 4.16 - Prob. 1PCh. 4.16 - Prob. 2PCh. 4.16 - Prob. 3PCh. 4.16 - Prob. 5PCh. 4.16 - Prob. 7PCh. 4.16 - Prob. 8PCh. 4.16 - Prob. 9PCh. 4.16 - Prob. 10PCh. 4.16 - Prob. 11PCh. 4.16 - Prob. 12PCh. 4.16 - Prob. 13PCh. 4.16 - Prob. 14PCh. 4.17 - Prob. 1PCh. 4.17 - Prob. 2PCh. 4.17 - Prob. 3PCh. 4.17 - Prob. 4PCh. 4.17 - Prob. 5PCh. 4.17 - Prob. 7PCh. 4.17 - Prob. 8PCh. 4 - Prob. 1RPCh. 4 - Prob. 2RPCh. 4 - Prob. 3RPCh. 4 - Prob. 4RPCh. 4 - Prob. 5RPCh. 4 - Prob. 6RPCh. 4 - Prob. 7RPCh. 4 - Prob. 8RPCh. 4 - Prob. 9RPCh. 4 - Prob. 10RPCh. 4 - Prob. 12RPCh. 4 - Prob. 13RPCh. 4 - Prob. 14RPCh. 4 - Prob. 16RPCh. 4 - Prob. 17RPCh. 4 - Prob. 18RPCh. 4 - Prob. 19RPCh. 4 - Prob. 20RPCh. 4 - Prob. 21RPCh. 4 - Prob. 22RPCh. 4 - Prob. 23RPCh. 4 - Prob. 24RPCh. 4 - Prob. 26RPCh. 4 - Prob. 27RPCh. 4 - Prob. 28RP
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