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## Lab 3 Review for AGEC622

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**Lab 3 Review for AGEC622**Adapted from review 2010,class notes and old exams**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**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**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**(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**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**Disassembly Problem**Component 1 Raw Product 1 Component 2 Raw Product 2 Component 3**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**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**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)