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

Week 5 Review LP Solution 1 Examples Understanding LP

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

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.

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?

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

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

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

Time Assignment Problem

Global optimal solution found. Objective value: Total solver iterations: 2 Variable Value Reduced Cost S D A E G Row Slack or Surplus Dual Price TIME UTILITY

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