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 à Model à Results à 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.