Chapter 2 Optimization & LP

What is a binding constraint?

Binding constraints uses up resources.

3 ways of expressing constraints

Less than or equal to; greater than or equal to; equal to.

Constraints must...

Be less than or equal to, greater than or equal to, or equal to some specific value.

Goals for spreadsheet design

Communication, Reliability, Auditability, Modifiability

What are the two ways to complete a problem?

Graphically/Enumeration or Mathematically (simplex method; excel)

How do you solve a max problem?

Move as far away from origin while touching feasible region

A greater than or equal to constraint can be expressed mathematically as?

f(x1, x2....Xn)>=B

When the objetive function can increase without ever contacting a constraint the LP model is said to be?

unbounded

Steps to SOLVE

1. plot boundary line of each constraint. 2. Identify the feasible region that satisfies all constraints. 3. locate the optimal solution by either plotting one or more level curves for obj. function and determine the direction in which parallel shifts in this line produce IMPROVED obj fuction values. OR Identify the coordinates of all extreme points of the feasible region and calc the obj function values associated with each point. Bounded feasible region the point with best obj function value is the optimal

What are the 4 steps of formulation?

1. understand the problem 2. identify the decision variables 3. state objective function as a linear combo of variables 4. state constraints as linear combos. 5 identify upper and lower bounds on decision variables.

A set of values for the decision variables that satisfy all constraints and yields the best objective function is?

A feasible solution and a corner point solution

What are the 4 special conditions?

Alternate optimal solutions, redundant constraints, unbounded solutions and infeasibility.

unbounded solution

Corner point method WONT work for this

What are the components of optimization problem?

Decisions, restrictions/constraints and objectives

What are other applications of MP?

Determining Product mix, manufacturing, routing and logistics, financial planning.

optimzation

Mathematical Programming driving force behind prescriptive analytics

What is the main application of MP?

Maximizing profit; minimizing cost

What is the objective function coefficient?

Might represent the marginal profits (or costs) associated with the decision variables. ex) C1X2+C2X2

How do you solve a min problem?

Move as close to the origin while touching feasible region

Level curves are used when solving LP models using the graphical method. To what part of the model do level curves relate?

Objective function

A facility produces two products and wants to maximize profit. The objective function to maximize is z=350x1+300x2. The number 300 means that

One unit of product 2 contributes $300 to the objective function

A facility produces two products. The labor constraint (in hours) is formulated as: 350x1+300x2<=10,000 The number 10,000

There are 10,000 hours of labor available for use.

Which of the following actions would shrink the feasible region of an LP model?

Tightening the constraints

Of the 4 special conditions which two prevent us from solving?

Unbounded solutions and infeasibility.

Decision variables

Usually defined as the variables in models. x1 x2 x3

Where is the optimal solution found?

Where boundary lines of constraints intersect. Corner points or Extremes points

In a mathematical forumation of an optimization problem, the objective function is written as z=2x1+3x2. Then

X1 is a decision variable

A mathematical programming application employed by a shipping company is most likely?

a routing and logistics problem.

Mathematical Programming

area of business analytics that finds the optimal or most efficient way of using limited resources to achieve the objective of an individual.

Limited resources are modeled in optimzation problems as

constraints

The number of units to ship from chicago to memphis is an example of

decision.

What are the three common elements of an optimization problem

decisions, constraints and objective

A production optimization problem has 4 decision variables and a requirement that at least b1 units of material 1 are consumed. Which of the following constraints reflects this fact?

f(x1, x2, x3, x4)>=b1

Objective function

identifies some function of the decision variables that the decision maker wants to either maximize or minimize

Level Curves

lines representing 2 obj functions values. 2 level curves are PARALLEL.

Suppose that a constraint 4x1+6x2>=1,800 is binding. Then a constraints 2x1+3x2>=600 is?

redundant

formulating model

taking a practical problem and expressing it algebraically

Feasible region

the intersection of the graphs in a system of constraints; all constraints are satisfied.

A linear forumlation means that

the objextive function and all constraints must be linear