172A-1 - Economics 172A 172A Introduction to Operation...

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Economics 172A Introduction to Operation Research (Part A) 1. Introduction inter 2010 Winter 2010 Herb Newhouse 1 eadings Readings • Hillier & Lieberman (9 th edition) – Ch. 1: Intro. 1.1 – 1.3. (We will not use H&L’s OR Courseware.) – Ch. 2: Overview of the Operations Research Modeling Approach – 2.1: Defining the Problem and Gathering Data. 2F lt i Mth t i lMdl – 2.2: Formulating a Mathematical Model. – 2.3: Deriving Solutions from the Model. – (The rest of chapter 2 is important in practice but will not be overed on exams.) covered on exams.) – Ch. 3: Introduction to Linear Programming – 3.1: Prototype Example. – 3.2: The Linear Programming Model. – 3.3: Assumptions of Linear Programming. – 3.4: Additional Examples. – 3.5: Formulating the Model on a Spreadsheet. 2 utline Outline eview Review – Linear equations. evel curves – Level curves. – 100A style constrained optimization. • Introduction to linear programming. – Formulating decision problems. – Examples. 3 eview Review 4
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Linear Functions, Equations and Inequalities • A linear function is a function of degree one and can be represented by a straight line when it comprises just two ariables variables. • A linear equation (inequality) is a linear function set equal (unequal) to a constant. • Examples: 2 3 5 : linear function xyz ++ 23 5 : non-linear function 2 3 5 89 : linear equation 3 5 89 : linear inequality x xy z ++= +≤ 2358 9 : linear inequality x yz ++≤ 5 raphing Linear Equations Graphing Linear Equations A linear equation involving two variables corresponds to qg p a straight line in a two dimensional plane. • Two methods for graphing – Slope-intercept ax by c += , where is the slope and is the intercept. ac a c yx b b b =− + – Intercept form bb b c c 1, where is the intercept and the . ab xy x y cc a b 6 22 0 HL (, 0 ) L H 7 0 , 4 7 6 0 H L + ≤+ 43 2 , ( , 0 ) H L L 8 H
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evel Curves Level Curves •O bjective function is not an equation.
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172A-1 - Economics 172A 172A Introduction to Operation...

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