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Agenda of Week VII. LP V LP Application 2 Time assignment Beggar family LINGO illustration Understanding LP LP interpretation Week 6 1 LP Sensitivity Analysis 3 Contribution coefficients RHS Examples

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Week 6 Review Understanding LP LP Interpretation 1 Objective function Decision variables Slack and surplus Shadow price Shadow cost

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Beggar Family Problem Maximization of Income from Collecting by Adjusting the Frequency of Collecting Activities by 3 Sons

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Beggar Family Problem Global optimal solution found. Objective value: 740.0000 Total solver iterations: 2 Variable Value Reduced Cost F 100.0000 0.000000 S 0.000000 3.500000 T 120.0000 0.000000 Row Slack or Surplus Dual Price OBJECTIVE 740.0000 1.000000 T-money 0.000000 1.000000 Lunchbox 0.000000 0.5000000

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Time Assignment Problem

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Global optimal solution found. Objective value: 112000.0 Total solver iterations: 2 Variable Value Reduced Cost S 53.33333 0.000000 D 26.66667 0.000000 A 0.000000 200.0000 E 0.000000 0.000000 G 0.000000 100.0000 Row Slack or Surplus Dual Price 1 112000.0 -1.000000 TIME 0.000000 -400.0000 UTILITY 0.000000 -100.0000

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Lingo Illustration o Beggar family problem Solving and interpretation o Time assignment problem Solving and interpretation

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LP Sensitivity Analysis o Objective Coefficient Ranges Interval of contribution coefficients changeable keeping current structure of optimal solution o Right-hand Side Ranges Interval of RHS changeable keeping current structure of optimal solution

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Beggar Family: Sensitivity Analysis Ranges in which the basis is unchanged: Objective Coefficient Ranges Current Allowable Allowable Variable Coefficient Increase Decrease F 5.000000 3.000000 3.000000 S 4.000000 3.500000 INFINITY T 2.000000 3.000000 0.5250000 Righthand Side Ranges Row Current Allowable Allowable RHS Increase Decrease POTATO 520.0000 360.0000 300.0000 TOKEN 440.0000 600.0000 180.0000

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Time Assignment: Sensitivity Analysis Ranges in which the basis is unchanged: Objective Coefficient Ranges Current Allowable Allowable Variable Coefficient Increase Decrease S 1000.000 0.0 INFINITY D 2200.000 0.0 1200.000 A 1800.000 INFINITY 200.0000 E 1500.000 INFINITY 0.0 G 1200.000 INFINITY 100.0000 Righthand Side Ranges Row Current Allowable Allowable RHS Increase Decrease TIME 80.00000 53.33333 35.55556 UTILITY 800.0000 640.0000 320.0000

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LP EXAMPLES.

LP EXAMPLES.

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