1. LP: Summary thus far Requirements Graphical solutions Excel Sensitivity Analysis

2. Requirements of a Linear Programming Problem Objective Function: LP problems seek to maximize or minimize some quantity. Constraints: restrictions that limit the degree to which we can pursue our objective. Alternative courses of action. Linear equations or inequalities.

3. Graphical Solutions for LP Must be no more than 2 decision variables. Plot the limits of the constraints. Find the feasible region. Determine the optimized solution (using corner point method or iso-profit line method).

4. Graphical Solutions for LP: Corner Point Method Theory behind LP states that the optimal solution to any problem will lie at a corner point, or extreme point of the feasible region. Find result for each corner of the feasible region, pick the one that best satisfies the goal (within reason).

5. Graphical Solutions for LP: Iso-Profit Line Method Find the slope of the optimization equation: For a given profit level, there will be a (infinite) # combinations of X 1 & X 2, described as a line. An iso-profit line that is farther from the origin (0,0) will have a greater profit level. Find the intersection of the iso-profit slope with the farthest point of the feasible region.

6. Spreadsheet Solutions for LP: MS Excel Formulate the optimization equation and the constraints. Build spreadsheet with formulas showing the relationships between the various elements. Using MS Excel Solver, define the cell to optimize, and the constraints on it.

7. Using MS Excel for LP: Answer Report Binding & non-binding constraints Slack

8. Using MS Excel for LP: Sensitivity Analysis Reduced Cost: how much a coefficient would need to change to affect the optimal solution. (Ignore sign) Allowable increase & decrease: how much a coefficient can change without changing the optimal combination for the solution (but it can change the actual optimized value)

9. Using MS Excel for LP: Sensitivity Analysis Shadow Price: How much, per unit, the constraint affects the optimized value Allowable increase & decrease: In what range does the shadow price hold true.

10. Using MS Excel for LP: Sensitivity Analysis All data in the sensitivity analysis are based on changing ONE THING AT A TIME.

11. Using MS Excel for LP: Troubleshooting Infeasibility: two possibilities: –An answer cannot be found that satisfies all constraints. –Part of the LP was input incorrectly. (More likely) Unboundedness: –An answer has no limit to its goal. –Part of the LP was input incorrectly. (See above)

12. Using MS Excel for LP: Example James Beerd and his cakes. GO TOGO TO

13. Using MS Excel for LP: Group Exercise Fill in the formulas Detail the constraints, etc. GO TO SPREADSHEET

14. Using MS Excel for LP: Homework pg. 55 #5: solve w/ MS Excel, discuss answer report & sensitivity report. pg. 59 #14, part A: solve w/ MS Excel, discuss answer report & sensitivity analysis. Turn in printout of solved spreadsheet, and email or hand in on diskette the Excel files by BEGINNING OF CLASS Thursday, Sept. 10