Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Expert Solution & Answer
Chapter 4, Problem 5RP
Explanation of Solution
Optimal solution:
- Consider the following linear programing problem:
- min z= -x1-2x2
- Subject to the constraints:
- 2x1+x2 ≤ 5
- x1+x2 ≤ 3
- x1,x2 ≥ 0
- Convert the minimization into maximization, then the result is:
- max z = -min(-z)
- max z = -min z*
- Therefore, the objective function is, max z* = x1+2x2
- Consider s1 and s2 are the two slack variables.
- Add each of the slack variables to each constraint when they are less than or equal to type.
- Here, the given two constraints are less than or equal to type, then these two slack variables are added to make it as standard form and at the same time add these variables to the objective function with 0 quantity weight.
- Therefore, the standard form of the LP is as follows:
- min z= -x1-2x2-0×s2
- Subject to the constraints:
- 2x1+x2 +s1= 5
- x1+x2+s2 = 3
- The matrix form is as follows:
- max z*=cX
- Subject to the constraints:
- AX=b
- The initial simplex table is shown below:
- In the initial simplex table, the first row is filled with objective function coefficients, second and third columns are filled with matrix A values.
- Basic variable column is filled with matrix b...
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The
following table belongs to the optimal solition nit
of a Lineer Programming Problem. Obtain the formulation of
the initial
problem.
XI
x2
ke
-Jig
38
X₁
Xu
O
1
O
19
41
14
23
38
xu
O
O
1
VI
38
A
38
AL
A2
(1-38M) (2-19M)
38
19
-3
38
5
L
응급
31
19
19
solution
7'
2
5
Solve the following problem and find the optimal solution.
K = 0, L = 18
Write and solve the following linear program using lingo, take screen shots of your model as well as the reports and the optimal solution. Clearly show the optimal solution.NB:K=the second digit of your student number;L=sum of the digits of your student number, For example if your student number is 17400159 thenK=7andL=1+7+4+0+0+1+5+9=27!!!! SAVE YOUR FILE BY YOUR STUDENT NUMBER!!!!minz=t∈T∑(AtYt+PtXt)+k∈K∑(HkUk+BkVk)s.t.Uk+Vk=50∀k∈KXt−CtYt<=0∀t∈Tk∈K∑Vk≥80t∈T∑Xt≥t∈T∑DtXt>=0∀t∈TYt∈{0,1}∀t∈TUk>=0∀k∈KVk>=0∀k∈KThe sets parameters and data are as follows: \[ \begin{array}{l} \mathrm{T}=\{1,2,3,4\} \\ \mathrm{K}=\{0,1,2,3,4\} \\ \mathrm{A}=\{5000,7000,8000,4000\} \\ \mathrm{D}=\{250,65,500,400\} \\ \mathrm{C}=\{500,900,700,800\} \\ \mathrm{P}=\{20, \mathrm{~L}, 25,20\} \\ \mathrm{H}=\{5,3,2, \mathrm{~K}, 9\} \\ \mathrm{B}=\{8,5,4,7,6\} \end{array} \]
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
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.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%.arrow_forwardQ1: 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 formarrow_forwardWhich of the following algorithms can be used to find the optimal solution of an ILP?(a) Enumeration method;(b) Branch and bound method;(c) Cutting plan method;(d) Approximation method.arrow_forward
Recommended textbooks for you
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole