Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Expert Solution & Answer
Chapter 4, Problem 6RP
Explanation of Solution
Optimal solution:
- Consider the following linear programing problem:
Subject to the constraints:
- From the linear
programming problem, it can be observed that one constraint is less than or equal to type and two constraints are greater than or equal to type. - Add the surplus variable e1 to the constraints greater than or equal to type constraints and add slack variables s1,s2 to the constraints less than or equal to type.
- Therefore, the standard form of linear programming problem is as follows:
- Max z = x1+x2-Ma1
Subject to the constraints:
The basic feasible solution is,
- Since basic feasible solution contains artificial variable,
- The artificial variable is eliminated
Expert Solution & Answer
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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 problem and find the optimal solution.
b) Consider the following linear programming problem:
Min z = x1 + x2
s.t. 3x1 – 2x2 < 5
X1 + x2 < 3
3x1 + 3x2 2 9
X1, X2 2 0
Using the graphical approach, determine the possible optimal solution(s) and comment
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Chapter 4 Solutions
Operations Research : Applications and Algorithms
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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- Which 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_forwardThe shaded region in the given figure above illustrates an unbounded feasible region. Which of the following is true? I. The maximum value for the objective function does not exist in an unbounded feasible region. II. If the objective function is Min Z=x+y, then it's maximum is 25 at (25,0). III. If the objective function is Max Z=-x+2y, then it's minimum is O at (25,0). IV. Unbounded feasible regions have either maximum or minimum value. 024 10 (25 0) -20 -10 10 O A. I O B. II O C.I and II O D. II and IVarrow_forward
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