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AGEC 352 Exam One Study Guide: Exam Format: Fifty Minutes 30 Questions Type of Questions: Multiple Choice and True/False Topics Chronologically: Lecture 1: Algebra Review Linearity and slope. Graphing linear functions (graphing feasible space and objective). Interpretation of algebraic equations and inequalities (interpreting constraints). Intersection of lines (corner points). Lab Handout 1: Spreadsheet Review Formulas and cell references. Graphing relationships with XY (Scatter). Sumproduct formula. Lecture 2: Microeconomic Review Optimization and how it supports equilibrium. Production Possibilities frontier and isorevenue line. Isoquant and isocost line. Indifference curve and budget line. Lecture 3: Introduction to Modeling Overview of the Modeling Process. Mgmt. Problem Model Results Decisions Arrow 1: Abstraction Arrow 2: Analysis Arrow 3: Interpretation Essential Questions of Modeling Background/History of LP Benefits and Advantages of Modeling Lab Handout 2: Modeling Process (Simon Pies Case) Simple to more complex models Analysis of results Making profit maximizing decisions on pie price Lecture 4: Spreadsheet Modeling Basics Expanded the Simon Pies model Class was cut short (not responsible for slides 7-10 of Lecture 4. Lab Handout 3: Spreadsheet Model of Santa Rosa Raisins Case Analysis of two decisions (raisin price and grape purchasing) Questions from Homework 3. Lecture 5: Beginning LP: Simple Constrained Optimization Basic rules of effective modeling Objective equation and variable Decision variables Limiting resources and constraints Exogenous, parameter, coefficient Checking the optimality of the solution Reading: Handouts on the website (Oprah/Dwight’s study time, Simon Pies Calculus) Lecture 6: Optimization Basics Linear Programming (LP) versus finding function maximums Objective equation properties Constraint properties Feasibility and Feasible Space Map of combinations of the activities to be considered Constraint Types Economic limits Policy limits Physical limits Activity (decision variables) types Representation in the objective function (unit payoffs) Representation in the constraints (unit requirements) Lab Handout 4: LP Setup Steps Algebraic form (max Y =…, subject to …) Line by line interpretation of algebraic form Graphing the feasible space Non-negativity constraints Corner points and finding the objective by enumeration Lecture 7: Minimization Problems Alternative (reversed) feasible space Solution strategies Introduction to MS Excel’s Solver Lecture 8: Linear Programming Objective Functions Objective variable as the primary goal Direct versus indirect constraining of variables Graphing the objective equation Level curves (three variables in two dimensions) Exact direction of improvement for objective variables Graphical solution methods Lab Handout 5: Solving LP in MS Excel Finding and interpreting the optimal LP solution Analysis of the solution by: Increasing the RHS of constraints Forcing activities optimally set to zero into the solution Lecture 9: LP Solutions and Sensitivity Three pieces to an optimal solution A) Objective variable value B) Decision variable levels C) Set of binding constraints Sensitivity Results Shadow prices When they are non-zero Questions answered by shadow prices Objective Penalties (Excel’s reduced costs) When they are non-zero Questions answered by shadow prices Ranges for Constraints Allowable increase or decrease to LHS for which shadow price is same Ranges for Objective Equation Allowable increase or decrease to objective coefficients for which decision variables do not change Problem Revision from Sensitivity Information Adding a hired labor activity e.g. Lecture 10: LP Solutions and Model Extensions Sensitivity of the optimal solution Unique versus multiple solutions Non-negativity constraints importance in the problem Purchasing activities Selling activities Model Extensions for Realism (Simulation) Transfer rows Lab Handout 6: Interpreting Sensitivity Results Reporting and interpreting all sensitivity information Terms: Exogenous (Variable) Endogenous (Variable) Decision Variable Parameter Objective (Variable) Linear Program Sensitivity Analysis Counterfactual Optimization Model Optimize Optimal Decision Optimal Solution Constraint Binding Constraint Objective Function Constrained Optimization Model Inequality Constraint Right-hand Side Left-hand Side Non-negativity Conditions Feasible Decision Linear Function Surplus Slack Feasible Region Constraint Set Feasible Solution Corner Point Technical Coefficients Parameters Shadow Price Allowable RHS Range Objective Coefficient Ranges Key Items and Concepts Overview of the Economic Modeling Process Getting from a managerial situation to making a decision The role of analysis in refining a model before recommending a decision Essential Questions to be Answered before Building a Model Benefits of Modeling Identifying the price to set to achieve maximum profits. Using either the profit graph or the revenue and costs graphs. The importance of model revision (e.g. adding a downward sloping demand curve or using actual cost data to add a linear cost equation to the model.) Using differential calculus to solve problems for exact optimal decisions. Basic Rules for Effective Modeling The Study Time Example Collection of data and determining technical coefficients How is data on grades and hours used to determine grade/per hour? Defining the decision problem What is to be maximized? What are the activities competing for resources? What are the limiting resources? Solving a problem with a single limiting constraint using the objective function coefficients. Identifying optimal decisions to achieve maximum profits (graphically). Optimization If profits are graphed as an inverted U, what does a horizontal tangent line indicate? Why is it not optimal to be a little to the left or right of the point of tangency? Linear Programming optimization 2 output and 2 limiting resources LP example (Tables and Chairs) Standard algebraic form of an LP problem. Graphical depiction of the feasible space. Graphical depiction of the objective equation. Intersection of constraints and corner points. What is the importance of corner points? Constraints Why are they important? Economically? Mathematically? What types of constraints are relevant in an LP? What do the coefficients on decision variables in a constraint mean? Given a single constraint, what is the maximum level for activities? Given several constraints, which one is most limiting for a given activity? How do you interpret the constraint graphed as a line? How do you interpret the area on either side of the graphed constraint? What does it mean to change the coefficients of a constraint? What does it mean to change the RHS of a constraint? In a two-output product mix model, what is the smooth curve from economic principles that is analogous to the LP feasible space? In a two-input demand model (like the diet model) what is the smooth curve from economic principles that is analogous to the LP feasible space? Minimization How do the constraints of minimization problems generally differ from that of maximization problems? How does the feasible space typically differ from that of a maximization problem? Finding a feasible combination given the constraints of a problem. How many feasible points are considered when determining optimality? Solving for the intersection of two lines. Objective Equations/Functions What does an objective function look like in a Graphical LP? What are the coefficients of an objective function in LP? Given an objective function, which direction does it improve? LP Solutions What are the primary components of an LP solution? What is the importance of LP sensitivity information? Objective coefficient ranges? Objective Penalties (under reduced costs in Excel)? Shadow prices? Constraint ranges? Does changing the RHS of a binding constraint change the value of optimal decision variables typically? Does changing a coefficient of the objective equation change the optimal decision variables typically? How do you interpret shadow prices? Interpretation of shadow prices for a >= and a <= constraint. Interpretation of allowable increase and decrease of objective coefficients. Interpretation of allowable increase and decrease of RHS of constraints. Interpretation of the ‘Penalty Cost’ (or reduced cost) of a decision variable.