Managerial decision modeling with spreadsheets by stair render chapter 02

Properties of LP Models1 Seek to minimize or maximize 2 Include “constraints” or limitations 3 There must be alternatives available4 All equations are linear... Example LP Model Formulat

Chapter 2 Linear Programming Models:

Graphical and Computer Methods

Steps in Developing a Linear

Properties of LP Models

1) Seek to minimize or maximize

2) Include “constraints” or limitations

3) There must be alternatives available4) All equations are linear

Example LP Model Formulation:

The Product Mix ProblemDecision: How much to make of > 2 products? Objective: Maximize profit

Constraints: Limited resources

Example: Flair Furniture Co.

Two products: Chairs and Tables

Decision: How many of each to make this

month?

Objective: Maximize profit

Flair Furniture Co Data

• Make no more than 450 chairs

• Make at least 100 tables

Decision Variables:

T = Num of tables to make

C = Num of chairs to make

Objective Function: Maximize Profit

Maximize $7 T + $5 C

Graphical Solution

• Graphing an LP model helps provide

insight into LP models and their solutions

• While this can only be done in two

dimensions, the same properties apply to all LP models and solutions

1 C = 1

00 0

0 100 500 800 T

C

1000

600 450

5 C = $ 2,1 00

7T +

5 C = $ 4,0 40

Optimal Point (T = 320, C = 360)

7T +

5 C = $ 2,8 00

T = 300, C = 375

LP Characteristics

• Feasible Region: The set of points that

satisfies all constraints

• Corner Point Property: An optimal

solution must lie at one or more corner

points

• Optimal Solution: The corner point with

the best objective function value is optimal

Special Situation in LP

1 Redundant Constraints - do not affect

the feasible region

Example: x < 10

x < 12The second constraint is redundant

because it is less restrictive

Special Situation in LP

2 Infeasibility – when no feasible solution

exists (there is no feasible region)

Example: x < 10

x > 15

Special Situation in LP

3 Alternate Optimal Solutions – when

there is more than one optimal solution

6

2T + 2C = 2 0 All points on

Red segment are optimal

Special Situation in LP

4 Unbounded Solutions – when nothing

prevents the solution from becoming

Using Excel’s Solver for LP

Recall the Flair Furniture Example: