This preview shows pages 1–7. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Algebra Day!!! courtesty of xkcd.com Ostrowski () Lecture 3 Jan 13 1 / 19 Homework!!! If you have not already, register for the course webpage (on gmail). Do this by emailing my your address with the subject msci 331. Homework is posted online (due Tuesday)! I will not give it to you any other way, so register today! (Note: if a instructor ever asks you for an email, maybe you shouldnt send it during that instructors class... at least pretend to care :) ) Ostrowski () Lecture 3 Jan 13 2 / 19 A review Recall Giapettos workshop problem Decision Variables: x : number of soldiers y : number of trains Objective: 2x + y Constraints: Finishing Constraint: 3x + 2y 80 Carpentry Constraint: 3x + 1y 50 Material Constraint: 1x + 2y 60 Bounds: x , y Ostrowski () Lecture 3 Jan 13 3 / 19 Finding a solution in 2d 10 20 30 40 50 4 8 12 16 20 24 3x + y 50 x + 2y 60 3x + 2y 80 Figure: Feasible Region for Giapetto If an optimal solution exists, it is always a vertex in the feasible region ! We can solve LPs graphically for only 23 variables. How do we go about solving larger problems? Ostrowski () Lecture 3 Jan 13 4 / 19 A bad idea We know if an optimal solution exists that it will be at a vertex. Idea : Enumerate all the vertices of the feasible region. In Giapettos problem, we have two variables. How many constraints do we need to define a single point in 2dimensions? Ostrowski () Lecture 3 Jan 13 5 / 19 A bad idea We know if an optimal solution exists that it will be at a vertex. Idea : Enumerate all the vertices of the feasible region. In Giapettos problem, we have two variables....
View Full
Document
 Winter '09
 Ostrowski

Click to edit the document details