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CDAE 266 - Class 17 Oct. 14 Last class: 3. Linear programming and applications Project 2

CDAE 266 - Class 17 Oct. 14 Last class: 3. Linear programming and applications Project 2 Quiz 5 ( take-home and due 5:00pm, Monday, Oct. 23 ) Today: Results of Quiz 5 and problem set 3 3. Linear programming and applications Review for the midterm exam

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CDAE 266 - Class 17 Oct. 14 Last class: 3. Linear programming and applications Project 2

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  1. CDAE 266 - Class 17 Oct. 14 Last class: 3. Linear programming and applications Project 2 Quiz 5 (take-home and due 5:00pm, Monday, Oct. 23) Today: Results of Quiz 5 and problem set 3 3. Linear programming and applications Review for the midterm exam Project 2 Next class: Midterm exam (10:55am – 12:20pm)

  2. CDAE 266 - Class 17 Oct. 24 Readings: Important dates: Midterm exam, Thursday, Oct. 26 Revision of project 1, due today Project 2 (case 1 on page 22), due Tuesday, Oct. 31

  3. N = 44 Range = 4 – 10 Average = 8.64 Result of problem Quiz 5

  4. N = 45 Range = 69 – 99 Average = 88.2 Result of problem set 3

  5. 3. Linear programming & applications 3.1. What is linear programming (LP)? 3.2. How to develop a LP model? 3.3. How to solve a LP model graphically? 3.4. How to solve a LP model in Excel? 3.5. How to do sensitivity analysis? 3.6. What are some special cases of LP?

  6. 3.5. How to interpret computer reports and conduct sensitivity analysis? 3.5.3. Summary of sensitivity analysis (1) One objective function coefficient changes. (2) Two objective function coefficients change at the same time -- 100% rule (3) One RHS value changes (4) Two RHS values change at the same time -- 100% rule

  7. 3.6. What are some special cased of LP? 3.6.1. Multiple optimal solutions 3.6.2. Infeasible problems 3.6.3. Unbounded problems

  8. No point, simultaneously, lie above line and below lines and. 1 2 3 2 Infeasible LP 1 3

  9. Maximize the Objective Function The Feasible Region Unbounded LP

  10. Take home exercise Solve the following LP model in Excel and obtain the “answer report” and “sensitivity report” X1 = Number of space ray X2 = Number of zappers Maximize P = 8X1 + 5X2 subject to 2X1 + 1X2 < 1200 (plastic) 3X1 + 4X2 < 2400 (labor) X1 + X2 < 800 (total) X1 - X2 < 450 (mix) X1 > 0 X2 > 0

  11. Midterm exam 1. What will be covered in the exam? 2. What will be the format? 3. What are the study materials and practice problems? 4. What do you need to bring to the exam? 5. Suggestions

  12. Midterm exam 1. What will be covered in the exam? -- Chapter 1 – Chapter 3 -- Approximate distribution: Chapter 1 10 - 15% Chapter 2 35 - 45% Chapter 3 45 - 55%

  13. Midterm exam 2. What will be the format? -- Short-answer questions (e.g., quiz questions) -- Problems (e.g., develop a LP model) -- Graphical analysis (e.g., solve a LP model graphically) -- Questions based on computer outputs (e.g., quiz 5 questions)

  14. Midterm exam 3. What are the study materials and practice problems? Quiz 1 to Quiz 5 Class exercises Class examples Practice questions on pages 21 of the reading package Lecture notes (class 1 - class 16) Problem sets 1, 2 and 3 Project 1 and project 2* Reading materials a. The Time Value of Money b. Basic Economic Relations c. Linear Programming d. How to solve a LP model in Excel?

  15. Midterm exam 4. What do you need to bring to the exam? -- Your calculator -- A ruler will be helpful -- TVM tables will be provided -- Graph paper will be provided -- No formula sheet is needed

  16. Midterm exam 5. Suggestions

  17. Project 2 -- Format requirements (see the handout “Guideline for project reports”) -- Project report (3-4 page of text plus computer outputs) -- What is the business problem of the project? -- Procedures: (1) Develop a LP model (2) Solve the LP model in Excel  “answer report” and sensitivity report” (you need to do this ONLY once) (3) Evaluate each of the three options and their combinations (a) More treated straw (b) One more box of handles (c) More labor (d) (a) + (b) (e) (a) + (c) (f) (b) + (c) (g) (a) + (b) + (c) Your project report should address all the six problems listed in the end of the project.

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