Fundamentals of Optimization and Statistical Modeling

Optimization Problem and LP Relaxation

The objective function for an optimization problem is: Min 3x – 2y, with constraints x ≥ 0, y ≥ 0. x and y must be integers. Suppose that the integer restriction on the variables is removed. If so, this would be a familiar two-variable linear program; however, it would also be an example of an LP relaxation of the integer linear program.

Integers in Linear Programs

Integers cannot be used in linear programs.

• False

Simple Linear Regression Model

In a simple linear regression model, y = b0 + b1x + eb1, b1 represents the intercept.

Time Series Recurring Pattern

A time series that shows a recurring pattern over one year or less is said to follow a cyclical pattern.

Binary Integer Program Variables

In binary integer programs, the integer variables take only the values 1 and -1.

Definition of Linear Regression

What is the definition of Linear Regression according to our course textbook?

Linear Regression is a type of analysis that attempts to show the relationship between two variables. It is a linear approach to model the relationship between dependent and independent variables.

Examples of Integers

The following are integers: 1.2, 3.98, 3.21

• False

Solver's Graphing Feature

Two of the homework problems required the use of Solver's graphing feature to display the associated data cylinders.

• False

Linear Optimization Model Solutions

Some of the homework problems required finding a solution to a linear optimization model.

• True

Solver and Null Hypothesis

Once an optimal solution is found for a linear program, Solver requires the creation of the null hypothesis.

• False

GRG Nonlinear Use

The homework problems never required the use of “GRG nonlinear”.

• False

Simplified Calculus Model Toolkit

Some of the assigned homework problems required the use of the simplified calculus model toolkit.

• False

Career Impact of Linear Regression

Which chapter or concept do you think will have the most impact on your career? Why?

Definitely the linear regression chapter because it can be used to determine relationships between variables, calculate statistical significance, etc., which is something that is widely used in businesses.

Solver for Integer Linear Programs

Solver must not be used to solve integer linear programs.

• False

Linear Programming for Optimal Solutions

Linear programming is used to find the very best possible solution to a problem.

• True

Linear Programming for Business Locations

One of the assigned homework problems used linear programming to identify the locations of principal places of business (PPBs) for a bank holding company.

• True

Camm-Cochran-Fry Technique

Three of the assigned homework problems required the use of the Camm-Cochran-Fry technique to find feasible alternative solutions to linear programs.

• False