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LP: Summary thus far

LP: Summary thus far. Requirements Graphical solutions Excel Sensitivity Analysis. Requirements of a Linear Programming Problem. Objective Function : LP problems seek to maximize or minimize some quantity .

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LP: Summary thus far

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  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. • Linearequations 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 cornerpoint, 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 X1 & X2, 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 farthestpoint 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 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

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