lecture3 - Algebra Day!!! courtesty of xkcd.com Ostrowski...

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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 2-d 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 2-3 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 2-dimensions? 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....
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lecture3 - Algebra Day!!! courtesty of xkcd.com Ostrowski...

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