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Comprehensive Review for AGEC622: Mathematical Programming Concepts and Applications

Prepare for the AGEC622 exam with this detailed review. Cover essential sections from the textbook "Applied Mathematical Programming Using Algebraic Systems" by B.A. McCarl and T.H. Spreen. Focus on key chapters, such as assumptions, integer programming, transportation problems, and LP model basics. Understand concepts such as demand-supply balance, optimization, objective functions, and sensitivity analysis. Review problem examples, including feed and disassembly issues, essential for mastering mathematical programming in agricultural economics.

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Comprehensive Review for AGEC622: Mathematical Programming Concepts and Applications

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  1. Lab 3 Review for AGEC622 Adapted from review 2010,class notes and old exams

  2. Preperation To prepare for the exam: Read the relevant book sections Textbook: Applied Mathematical Programming Using Algebraic Systems by B. A. McCarl and T. H. Spreen http://agecon2.tamu.edu/people/faculty/mccarl-bruce/books.htm Look at Chapter 1 Assumptions • Look at Chapter 2 • Notable violation • Divisibility- Integer Programming

  3. Chapter 5 • Transportation (5.3) • Introduce a fundamental concept: demand and supply balance • Feed (5.4) • Joint Product (5.5) • Chapter 7 • Disassembly (7.2) • Chapter 15 • Integer

  4. The Basics of LP Models • What LP models are • Optimization over decision variables subject to constraints – Always an abstract of the real world • Obj. F(X) • S.t. G(X)ЄS • Example: • Max (93-60)Xeconomy+(198-150)Xregular+(255-200)Xfancy • S.t. 0.125Xeconomy+0.26Xregular+0.30Xfancy<=30 • 0.40Xeconomy+0.55Xregular+0.65Xfancy<=70 • Xfancy>=1 • Non-Negative • Versatility of LP models And Usage

  5. (cont.) • Objective function • Shadow price • homogeneity of units • Assumptions of the LP problem • Reduced cost • Prescriptive: What decisions should be made? • Predictive: Predict the consequence of environmental changes depicted by the parameters in the model • Sensitivity demonstration

  6. Transportation problem

  7. Problem Example (2008 Exam #1) • Obj. Max Profit=Revenue-Cost • Revenue= • Cost= Waste Disposal + Production Cost + Shipping Cost + Purchase Cost • Production Cost: YOH, YTX,, which determines the final output but constrained by input purchase • Shipping Cost: QME,OH QME,TX QWT,OH QWT,TX • Purchase Cost: BuyME, BuyTX

  8. Feed problem

  9. Feed Problem

  10. Disassembly Problem Component 1 Raw Product 1 Component 2 Raw Product 2 Component 3

  11. Assembly disassembly problem (exam 2010)

  12. Joint product Possibility 1 Possibility II . . . Three sets of variable: Purchase(Input), Production, Sale(output) Input Sale 1 Sale II . . . Demand-supply balance Demand-supply balance

  13. Class notes

  14. Integer Programming • (Chapter 15) • Why do we need integer programming? • Understand the use of indicator variable Can you tell the relationship between X and Z here? Under what circumstances will such condition be needed? Y

  15. Integer programming (Exam 2010) Here Y1 and Y3 must be purchased always since Y1+Y3=2. So, capacity of 0≤X1 ≤18 and the costs generated from using Y1 &Y3 are $8 and $3 respectively If Y2 is purchased, capacity of 0 ≤X2 ≤5 and the cost generated is $5. If Y2 is not purchased(Y2=0),X2 will not be produced (Solution 2009 exam)

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