11_hw1_sol

11_hw1_sol - MS&E 211 Fall 2011 Linear and Nonlinear...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Fall 2011 Linear and Nonlinear Optimization Oct 11, 2011 Prof. Yinyu Ye Homework Assignment 1: Sample Solution Problem 1 Let x 1 j = tons of waste sent to incinerator j from Palo Alto , x 2 j = tons of waste sent to incinerator j from Stanford, and y ij = tons of debris sent to landfill j from incinerator i . The LP model can be written as: min 3(60 x 11 + 9 x 12 + 35 x 21 + 41 x 22 + 5 . 5 y 11 + 7 . 5 y 12 + 9 . 5 y 21 + 6 . 5 y 22 ) +40( x 11 + x 21 ) + 30( x 12 + x 22 ) s.t. x 11 + x 12 = 1000 x 21 + x 22 = 700 y 11 + y 12 = 0 . 2( x 11 + x 21 ) y 21 + y 22 = 0 . 2( x 12 + x 22 ) x 11 + x 21 1000 x 12 + x 22 1000 y 11 + y 21 400 y 12 + y 22 400 x ij , y ij 0 , i = 1 , 2; j = 1 , 2 . Problem 2. Let x ijg be the number of grade g students in neighborhood i assigned to school j . Then we have: min I i =1 J j =1 d ij ( G g =1 x ijg ) s.t. I i =1 x ijg C jg , j, g J j =1 x ijg = S ig , i, g x ijg 0 , i, j, g. Problem 3.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/16/2012 for the course MS&E 211 at Stanford.

Page1 / 3

11_hw1_sol - MS&E 211 Fall 2011 Linear and Nonlinear...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online