5 Problems on the Deterministic Optimization - Project | ISYE 6669, Study Guides, Projects, Research of Systems Engineering

Material Type: Project; Class: Deterministic Optimiz; Subject: Industrial & Systems Engr; University: Georgia Institute of Technology-Main Campus; Term: Spring 2005;

Typology: Study Guides, Projects, Research

Pre 2010

Uploaded on 08/05/2009

koofers-user-wu1
koofers-user-wu1 🇺🇸

10 documents

1 / 3

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
ISyE 6669 Spring 2005 Mid-Term, Feb 24
1. (25 points) Consider the system of equations:
x1 - x2 - x3 = -4
x1 -3x2 = -6
(a) Does it have no solution, a unique solution, or an infinite number of solutions
(b) Plot the solution in 3 dimensions
Now add non-negativity constraints x1 > 0, x2 > 0, x3 > 0
(c) Plot the LP solution set (imposing the non-negativity constraints)
(d) Does the LP have an unbounded direction and if so, what is it?
2. (20 points) In the LP of problem (1.), suppose the objective is to minimize x1+
2x2+ x3. The optimum primal solution is x1 = 0, x2 = 2, x3 = 2. What is the optimum dual
solution? Plot the objective value vs. c1 where the current value of c1 = 1.
pf3

Partial preview of the text

Download 5 Problems on the Deterministic Optimization - Project | ISYE 6669 and more Study Guides, Projects, Research Systems Engineering in PDF only on Docsity!

ISyE 6669 Spring 2005 Mid-Term, Feb 24

  1. (25 points) Consider the system of equations: x 1 - x 2 - x 3 = - x 1 -3x 2 = - (a) Does it have no solution, a unique solution, or an infinite number of solutions (b) Plot the solution in 3 dimensions Now add non-negativity constraints x 1 > 0, x 2 > 0, x 3 > 0 (c) Plot the LP solution set (imposing the non-negativity constraints) (d) Does the LP have an unbounded direction and if so, what is it?
  2. (20 points) In the LP of problem (1.), suppose the objective is to minimize x 1 + 2x 2 + x 3. The optimum primal solution is x1 = 0, x2 = 2, x3 = 2. What is the optimum dual solution? Plot the objective value vs. c 1 where the current value of c 1 = 1.
  1. (20 points) Suppose we have a project with 5 activities and immediate predecessors and durations as given below: Activity Predecessors Durations A - 2 B - 3 C A 4 D A,B 6 Draw the network, solve for earliest and latest start times using longest path methods in an acyclic network, and identify which activities have positive float and give the total float for those activities.