Introduction to Algorithms
Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 29.3, Problem 5E
Program Plan Intro

To solve the linear program using SIMPLEX algorithm:

  Introduction to Algorithms, Chapter 29.3, Problem 5E

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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∑​(At​Yt​+Pt​Xt​)+k∈K∑​(Hk​Uk​+Bk​Vk​)s.t.Uk​+Vk​=50∀k∈KXt​−Ct​Yt​<=0∀t∈Tk∈K∑​Vk​≥80t∈T∑​Xt​≥t∈T∑​Dt​Xt​>=0∀t∈TYt​∈{0,1}∀t∈TUk​>=0∀k∈KVk​>=0∀k∈KThe sets parameters and data are as follows: \[ \begin{array}{l} \mathrm{T}=\{1,2,3,4\} \\ \mathrm{K}=\{0,1,2,3,4\} \\ \mathrm{A}=\{5000,7000,8000,4000\} \\ \mathrm{D}=\{250,65,500,400\} \\ \mathrm{C}=\{500,900,700,800\} \\ \mathrm{P}=\{20, \mathrm{~L}, 25,20\} \\ \mathrm{H}=\{5,3,2, \mathrm{~K}, 9\} \\ \mathrm{B}=\{8,5,4,7,6\} \end{array} \]
Using Python/PuLP solve   At the beginning of month 1, Finco has $400 in cash.  At the beginning of months 1, 2, 3, and 4, Finco receives certain revenues, after which it pays bills (see Table 2 below).  Any money left over may be invested for one month at the interest rate of 0.1% per month; for two months at 0.5% per month; for three months at 1% per month; or for four months at 2% per month.  Use linear programming to determine an investment strategy that maximizes cash on hand at the beginning of month 5.  Formulate an LP to maximize Finco’s profit.   Table 2 Month Revenues ($) Bills ($) 1 400 600 2 800 500 3 300 500 4 300 250
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