1. Chapter 4 - Linear Programming: Computer Solution Excel Solver

2. Computer Solution
Early linear programming used lengthy manual mathematical solution (Linear Algebra and Matrix Algebra) procedure called the Simplex Method.
Steps of the Simplex Method have been programmed in software packages designed for linear programming problems.
Many such packages available currently.
Used extensively in business and government.
Text focuses on Excel Spreadsheets.

3. Excel Spreadsheet for Beaver Creek Pottery Company Example
Excel Spreadsheets
Excel Spreadsheet for Beaver Creek Pottery Company Example

4. Excel Spreadsheet for Beaver Creek Pottery Company Example
Excel Spreadsheets
Excel Spreadsheet for Beaver Creek Pottery Company Example

5. Excel Model
When formulating a linear programming problem on an Excel spread sheet:
Parameters are called Data Cells.
Decision variables are called Variable Cells.
Right hand sides are part of the Constraints.
The objective function is called the Target Cell.

6. Excel Spreadsheets “Solver” Parameter Screen
Location of the Objective function value
Optimization Type
Location of the Decision Variables
Location of Constraints
Check the box of non-negativity
Press “Add” to add constraints
Choose Simplex LP

7. Excel Spreadsheets Adding Model Constraints

8. Check the box if integer constraint is not required

9. Excel Spreadsheets Solution Screen

10. Excel Spreadsheets Answer Report

11. Example Problem: Airplane Parts
Problem Statement
Two airplane parts: no.1 and no.2.
Three manufacturing stages: stamping, drilling, finishing.
Decision variables: x1 (number of part no.1 to produce)
x2 (number of part no.2 to produce)
Model: maximize Z = $650x x2
subject to
4x x2  105 (stamping,hr)
6.2x x2  90 (drilling, hr)
9.1x x2  110 (finishing, hr)
x1,x2  0

12. Example Problem: Airplane Parts Excel Spreadsheet Solution

13. Example Problem: Airplane Parts Excel Spreadsheet Solution

14. Excel Solver Exercise
Use Solver to solve the following LPP model with 6 decision variables and 7 functional constraints.
Minimize Z = 18x1 + 22x2 + 10x3 + 12x4 + 10x5 + 9x6
subject to
Constraint 1 2x2 + 2x3 + 2x4 + 5x5 + 3x6  200
Constraint 2 270x5 + 8x  300
Constraint 3 6x1 + 4x2 + 2x3 + 3x4+ x5  50
Constraint 4 20x1 + 48x2 + 12x3 + 8x4+ 30x5  4000
Constraint 5 3x1 + 4x2 + 5x3 + 6x4 + 7x5 + 2x6  200
Constraint 6 5x1 + 2x2 + 3x3 + 4x4  120
Constraint 7 90x x x3 + 90x4 + 75x5 + 35x6  4200
Non-negative All xj  0
Integer All xj are integers

15. Excel Solver Exercise: Excel Spreadsheet