1. Agenda of Week VI. LP IV LP Application 3 Time assignment Beggar family LINGO illustration Understanding LP LP Interpretation 2 Objective function Decision variables Slack and surplus Shadow price Shadow cost Solving Week 5 1

2. Week 5 Review LP Solution 1 Examples Understanding LP

3. LINGO Illustration o Time assignment problem Modeling the minimization problem Transformation to standard form Solution

4. LP Interpretation o Optimal objective function value o Optimal decision variable values o Reduced/Shadow cost Negative effects of decision variable 1 whose current value is 0. (-) reduced cost means the improvement of obj. func.

5. LP Interpretation o Slack Amount of resources remaining after optimal solution What kinds of resources should be paid more attention to when multiple resources are o Surplus Amount of provisions over minimum requirement in optimal solution What kinds of provisions should be paid more attention to?

6. LP Interpretation o Dual/Shadow Price Positive effect of additional 1 to obj, func. of resource whose slack is 0 Resources whose slack is greater than 0 shadow price is 0 Upper bound of willingness-to-pay for additional resources

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

8. 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

9. Time Assignment Problem

10. 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

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