Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Expert Solution & Answer
Chapter 6, Problem 5RP
a.
Explanation of Solution
Dual linear problem and its optimal solution
- The dual of a given linear
program is another linear program that is derived from the original linear program in following ways:- Each variable in the original linear program becomes a constraint in the dual linear program.
- Each constraint in the original linear program becomes a variable in the dual linear program.
- The objective direction is inversed which becomes maximum in the original and minimum in the dual.
- Hence the dual of the linear problem is
Subject to
- The formulas for
b.
Explanation of Solution
Range of values
- For a maximization problem, the new optimal value = (old optimal value) + (Constraint i’s shadow price).
- For a minimization problem, the new optimal value = (old optimal value) – (Constraint i’s shadow price)...
c.
Explanation of Solution
Range of values
- For a maximization problem, the new optimal value = (old optimal value) + (Constraint i’s shadow price).
- For a minimization problem, the new optimal value = (old optimal value) – (Constraint i’s shadow price)...
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Students have asked these similar questions
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: \[ \begin{array}{l} \mathrm{T}=\{1,2,3,4\} \\ \mathrm{K}=\{0,1,2,3,4\} \\ \mathrm{A}=\{5000,7000,8000,4000\} \\ \mathrm{D}=\{250,65,500,400\} \\ \mathrm{C}=\{500,900,700,800\} \\ \mathrm{P}=\{20, \mathrm{~L}, 25,20\} \\ \mathrm{H}=\{5,3,2, \mathrm{~K}, 9\} \\ \mathrm{B}=\{8,5,4,7,6\} \end{array} \]
Solve the following graphically:
Max z = 3x1 + 4x2
subject to x1 + 2x2 ≤ 16
2x1 + 3x2 ≤ 18
x1 ≥ 2
x2 ≤ 10
x1, x2 ≥ 0
What are the optimal values of x1, x2, and z?
Group of answer choices
x1 = 93, x2 = 0, z = 48
x1 = 19, x2 = 0, z = 32
x1 = 10, x2 = 0, z = 27
x1 = 9, x2 = 0, z = 27
x1 = 9, x2 = 3, z = 30
x1 = 12, x2 = 6, z = 42
QUESTION 9
What is one advantage of AABB over Bounding Spheres?
Computing the optimal AABB for a set of points is easy to program and
can be run in linear time. Computing the optimal bounding sphere is a
much more difficult problem.
The volume of AABB can be an integer, while the volume of a Bounding
Sphere is always irrational.
An AABB can surround a Bounding Sphere, while a Bounding Sphere
cannot surround an AABB.
To draw a Bounding Ball you need calculus knowledge.
Chapter 6 Solutions
Operations Research : Applications and Algorithms
Ch. 6.1 - Prob. 1PCh. 6.1 - Prob. 2PCh. 6.1 - Prob. 3PCh. 6.1 - Prob. 4PCh. 6.1 - Prob. 5PCh. 6.2 - Prob. 1PCh. 6.2 - Prob. 2PCh. 6.3 - Prob. 1PCh. 6.3 - Prob. 2PCh. 6.3 - Prob. 3P
Ch. 6.3 - Prob. 4PCh. 6.3 - Prob. 5PCh. 6.3 - Prob. 6PCh. 6.3 - Prob. 7PCh. 6.3 - Prob. 8PCh. 6.3 - Prob. 9PCh. 6.4 - Prob. 1PCh. 6.4 - Prob. 2PCh. 6.4 - Prob. 3PCh. 6.4 - Prob. 4PCh. 6.4 - Prob. 5PCh. 6.4 - Prob. 6PCh. 6.4 - Prob. 7PCh. 6.4 - Prob. 8PCh. 6.4 - Prob. 9PCh. 6.4 - Prob. 10PCh. 6.4 - Prob. 11PCh. 6.4 - Prob. 12PCh. 6.4 - Prob. 13PCh. 6.5 - Prob. 1PCh. 6.5 -
Find the duals of the following LPs:
Ch. 6.5 - Prob. 3PCh. 6.5 - Prob. 4PCh. 6.5 - Prob. 5PCh. 6.5 - Prob. 6PCh. 6.6 - Prob. 1PCh. 6.6 - Prob. 2PCh. 6.7 - Prob. 1PCh. 6.7 - Prob. 2PCh. 6.7 - Prob. 3PCh. 6.7 - Prob. 4PCh. 6.7 - Prob. 5PCh. 6.7 - Prob. 6PCh. 6.7 - Prob. 7PCh. 6.7 - Prob. 8PCh. 6.7 - Prob. 9PCh. 6.8 - Prob. 1PCh. 6.8 - Prob. 2PCh. 6.8 - Prob. 3PCh. 6.8 - Prob. 4PCh. 6.8 - Prob. 5PCh. 6.8 - Prob. 6PCh. 6.8 - Prob. 8PCh. 6.8 - Prob. 9PCh. 6.8 - Prob. 10PCh. 6.8 - Prob. 11PCh. 6.9 - Prob. 1PCh. 6.9 - Prob. 2PCh. 6.9 - Prob. 3PCh. 6.10 - Prob. 1PCh. 6.10 - Prob. 2PCh. 6.10 - Prob. 3PCh. 6.11 - Prob. 1PCh. 6.11 - Prob. 3PCh. 6.11 - Prob. 4PCh. 6.12 - Prob. 5PCh. 6.12 - Prob. 6PCh. 6.12 - Prob. 7PCh. 6 - Prob. 1RPCh. 6 - Prob. 2RPCh. 6 - Prob. 3RPCh. 6 - Prob. 4RPCh. 6 - Prob. 5RPCh. 6 - Prob. 6RPCh. 6 - Prob. 7RPCh. 6 - Prob. 8RPCh. 6 - Prob. 9RPCh. 6 - Prob. 10RPCh. 6 - Prob. 11RPCh. 6 - Prob. 13RPCh. 6 - Prob. 14RPCh. 6 - Prob. 15RPCh. 6 - Prob. 17RPCh. 6 - Prob. 18RPCh. 6 - Prob. 19RPCh. 6 - Prob. 20RPCh. 6 - Prob. 21RPCh. 6 - Prob. 22RPCh. 6 - Prob. 25RPCh. 6 - Prob. 29RPCh. 6 - Prob. 33RPCh. 6 - Prob. 34RPCh. 6 - Prob. 35RPCh. 6 - Prob. 36RPCh. 6 - Prob. 37RP
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