MAT 5340, Spring '12 (121) §101

Let us reflect that, having banished from our land that religious intolerance under which mankind so long bled and suffered, we have yet gained little if we countenance a political intolerance as despotic, as wicked, and capable of as bitter and bloody persecutions.

— Thomas Jefferson (1743-1826) in his First Inaugural Address.

Homework List

✈ Jump down to 'This Week.'

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Week 1

• Monday, Jan 16 — No classes
  ◊ Martin Luther King, Jr., Day
  
  
• Wednesday, Jan 18
  ◊ Read Chapter 1.
  ¤ Choose one the Edelman Award winners. Find the article describing the winner in the appropriate Jan-Feb issue of Interfaces (click the "Online Access" link near the bottom of the page), and write a paragraph or two summarizing the project.
  
  
• Friday, Jan 20
  ◊ Read Chapter 2.    (See the ClassNotes directory if you don't have your text yet.)
  
  

Week 2

• Monday, Jan 23
  §3.1. Pg 91: No 3.1-1, 4, 7; LA 3.1-6, 11.
  
  
• Wednesday, Jan 25
  §3.2. Pg 91: No 3.2-1, 2, 5; LA 3.2-3.
  
  
• Friday, Jan 27
  §3.3. Pg 91: No 3.3-1, 2.
  §3.4. Pg 91: No 3.4-5.
  
  

Week 3

• Monday, Jan 30
  §3.6. Pg 91: No 3.6-1, 4.
  
  
• Wednesday, Feb 1
  §4.1. Pg 150: No 4.1-1, 6, 8.
  
  
• Friday, Feb 3
  §4.3. Pg 150: No 4.3-4, 5.
       [4.3-4: Optimal Solution: \(Z = 70;\quad (x_1, x_2, x_3) = \left(0, 10, \frac{20}{3}\right) \).]
       [4.3-5: Optimal Solution: \(Z = \frac{4200}{19};\quad (x_1, x_2, x_3) = \left(0, \frac{450}{19}, \frac{480}{19}\right) \).]
  
  

Week 4

• Monday, Feb 6
  ◊ You can use the Online Simplex Tool to check your answers. (From http://www.zweigmedia.com/RealWorld/simplex.html.)
  ◊ Exercise:
  \(\quad\) Maximize: \(Z = 3x_1 + 2x_2 \)
  subject to:
  \( \quad\quad 2x_1+x_2 \le 18 \)
  \( \quad\quad 2x_1+3x_2 \le 42 \)
  \( \quad\quad 3x_1+x_2 \le 24 \)
  with \( x_i \ge 0 \)
  §4.4. Pg 150: No 4.4-5, 6.
  
  
• Wednesday, Feb 8
  §4.5. Pg 150: No 4.5-1, 2, 8.
  
  
• Friday, Feb 10
  §4.5. Pg 161: No 4.5-1, 3, LA 5.
  ◊ The following tableaux occured in simplex runs of various 2 variable, 2 constraint LPs. Determine whether the LP (a) is unbounded, (b) has multiple solutions, or (c) is degenerate.
  
  
  1. \( \begin{array}{|c| cccc |c|} z & x_1 & x_2 & s_1 & s_2 & RHS \\ \hline 1 & 0 & 3 & 2 & 0 & 20 \\ 0 & 1 & -2 & -1 & 0 & 4 \\ 0 & 0 & -1 & 0 & 1 & 2 \\ \hline \end{array} \) \(\qquad 2.\ \ \begin{array}{|c| cccc |c|} z & x_1 & x_2 & s_1 & s_2 & RHS \\ \hline 1 & 0 & -1 & 0 & 2 & 20 \\ 0 & 0 & 0 & 1 & -2 & 5 \\ 0 & 1 & -2 & 0 & 3 & 6 \\ \hline \end{array} \)
     
     
  3. \( \begin{array}{|c| cccc |c|} z & x_1 & x_2 & s_1 & s_2 & RHS \\ \hline 1 & 2 & 0 & 0 & 1 & 8 \\ 0 & 3 & 1 & 0 & -2 & 4 \\ 0 & -2 & 0 & 1 & 1 & 0 \\ \hline \end{array} \) \( \qquad 4.\ \ \begin{array}{|c| cccc |c|} z & x_1 & x_2 & s_1 & s_2 & RHS \\ \hline 1 & 0 & 0 & 2 & 0 & 5 \\ 0 & 0 & -1 & 1 & 1 & 4 \\ 0 & 1 & 1 & -1 & 0 & 4 \\ \hline \end{array} \)
     
     
  
  

Week 5

• Monday, Feb 13
  ◊ Web Mercantile, LLC, Warehouse Leasing Project (Due next Monday.)
  ¤ Maple pivot function:
     ☞   pivot := (M,i,j) -> LinearAlgebra[Pivot](LinearAlgebra[RowOperation](M,i,1/M[i,j]),i,j);
  \[ ( {M,i,j} )\mapsto {\it LinearAlgebra}_{{{\it Pivot}}} \left( {\it LinearAlgebra}_{{{\it RowOperation}}} \left( M,i,\frac1{M_{{i,j}}} \right) ,i,j \right) \]
  
• Wednesday, Feb 15
  ◊ The postoptimality spreadsheet (in the ClassNotes folder)
  ◊ The shadow price/reduced cost example
  §4.7. Pg 161: No 4.7-4, 6.
  
  
• Friday, Feb 17 — Elm Farm Ollie Day's eve
  ◊ Work on the project that's due Monday!
  ¤ Abstract, title, and information for our INFORMS poster project.
  
  

Week 6

• Monday, Feb 20
  §5.1. Pg 202: No 5.1-3, 9.
  
  
• Wednesday, Feb 22
  §6.1. Pg 276: 6-1.3 [Solve the primal and dual for (a). Set up the dual and compare to the primal for (b).]
  ◊ See the ClassNotes directory for copies of the examples.
  
  
• Friday, Feb 24
  § 8.1, 8.2. Read.
  
  

Week 7

• Monday, Feb 27
  §9.2 Pg 412: 9.2-1.
  
  
• Wednesday, Feb 29
  §9.3 Pg 412: 9.3-1.
  
  
• Friday, Mar 2
  ◊ Shortest Path Assigment: Due Monday, Mar 5.
  • Enter the commands below in Maple to produce your network. Then find the shortest path.
    randomize(your phone number with no spaces or dashes):
    with(GraphTheory): with(RandomGraphs):
    V := [S,b,c,d,e,f,g,h,i,j,k,T]:
    N := RandomNetwork(V, 0.35, weights=3..9, acyclic);
    DrawNetwork(N, S, T, horizontal, scaling=unconstrained);
  
  

Week 8

• Monday, Mar 5
  ¤ Groups: Propose the fourth "course area" for our project.
  
  
• Wednesday, Mar 7
  ¤ Groups: Propose the inputs and outputs for our project.
  
  
• Friday, Mar 9
  ◊ Look at our poster (in progress).
  
  

Spring Break Week

• Monday, Mar 12, to Friday, Mar 16
  ◊ Let's be careful out there! — Sgt Esterhaus
  
  

Week 9

• Monday, Mar 19
  ¤ Find more output factors for our study. ¤ Expand the CCR forms using:
  1. Number of DMUs is \(n=4\).
  2. Number of inputs \(x_{ij}\) is \(4\) for each DMU.
  3. Number of outputs \(y_{rj}\) is \(3\) for each DMU.
  (You don't need to insert surplus, slack, or artificial variables.)
  
  
• Wednesday, Mar 21
  ◊ Determine a monetary-based output factor for our project.
  ◊ See the ClassNotes folder for today's topics.
  
  
• Friday, Mar 23
  ◊ Work on the Take Home midterm due next Wednesday.
  ◊ NOTE: We used «Reduced cost» for «Penalty cost» (for Problem 3b).
  

Week 10

• Monday, Mar 26
  ◊ Work day! — focus on the Gen Ed project.
  
  
• Wednesday, Mar 28
  ¤ INFORMS Job listings
  
  
• Friday, Mar 30
  ◊ Focus on the Gen Ed project.
  
  

Week 11

• Monday, Apr 2
  ◊ Finish the decision tree for DT Co's new widget.
  
  
• Wednesday, Apr 4
  ◊ Finish data collection for the Gen Ed project.
  
  
• Friday, Apr 6
  
  

Week 12   ♘  (This Week)

• Monday, Apr 9
  ◊ Easter break — no classes
  
  
• Wednesday, Apr 11
  ¤ The poster set (tex, pdf, and Maple files) is on the web.
  
  
• Friday, Apr 13
  ¤ Read the first sections of "Interior Methods for Nonlinear Optimization" by Forsgren, Gill, & Wright
  
  

Week 13

• Monday, Apr 16
  ¤ Work day: read "Interior Methods;" work on your presentation
  ◊ Our project is presented in the poster session today at 2:45 pm.
  
  
• Wednesday, Apr 18
  ¤ Work day: read "Interior Methods;" work on your presentation
  
  
• Friday, Apr 13
  ¤ Presentations start Monday.
  ◊ See the Presentation Sources directory for files.
  
  

Week 14

• Monday, Apr 23
  
  • P Bare
  • T Conn
  • K Mikeal
  
  
• Wednesday, Apr 25
  
  • J Castonguay
  • S Moore
  
  
• Friday, Apr 27
  
  • J Winkler
  • S Yarbrough
  
  

Week 15

• Monday, Apr 30
  
  • T Williams
  • A Smith
  
  
• Wednesday, May 2
  
  • D Allworthy
  • D King
  
  
• Friday, May 4
  
  • J Cantrell
  • A Cox
  • A Grady
  
  

Week 16   ♘  (This Week)

• Thursday, May 4
  ¤ Final Exam: Due by 5:00 pm on 5/10/12      (\(\LaTeX\) source)
  ◊ Another technique to use on a network that's difficult to draw is:

   DV := [list of difficult vertices]:
   H := InducedSubgraph(N, DV); 
   DrawNetwork(H, style=circle);

  
  

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Last modified: Wednesday, 01-Feb-2023 08:32:12 EST

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