homework-1-solutions

homework-1-solutions - MthSc810 – Mathematical...

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

View Full Document Right Arrow Icon

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MthSc810 – Mathematical Programming Fall 2011, Solutions of Homework #1. 1 Relaxations and restrictions Provide two relaxations for each of the following problems: min 2 x + 3 y min x + y + z s.t. ≤ x ≤ 2 s.t. x- y + z = 0 1 ≤ y ≤ 4 x + 2 y + 3 z ≥ 4 x, y, z ≥ Solution. min 2 x + 2 y min x + y s.t. ≤ x ≤ 5 s.t. x- y + z ≤ ≤ y ≤ 4 x + 2 y + 3 z ≥ x, y, z ≥ min 2 x + 3 y min x + y + z s.t. ≤ x ≤ 2 s.t. x- y + z = 0 y ≥ x + 3 y + 3 z ≥ 4 x, y, z ≥ 2 Lower and upper bounds Given the following problem: min 2 x + 3 y s.t. x + y ≥ 3 1 ≤ x ≤ 4 1 ≤ y ≤ 3 – Is the solution ( x, y ) = (4 , 3) feasible? A.: Yes, because it satisfies the constraint and the variable bounds. – What is the corresponding value of the objective function? A.: 2 · 4 + 3 · 3 = 17. – Is it a lower or an upper bound on the optimum? A.: A feasible solution always gives an upper bound on the global optimum....
View Full Document

{[ snackBarMessage ]}

Page1 / 2

homework-1-solutions - MthSc810 – Mathematical...

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