EASTERN MEDITERRANEAN UNIVERSITY
Department of Industrial Engineering
IENG212/MANE212 Modelling and Optimization
HOMEWORK 4
Spring 2016-17
1. Find the shortest path from node 2 to all the nodes in the following network. Identify the shortest path
tree obtained.
cij
1
2
2
5
6
5
6
1
4
1
7
2
3
2
2
6
3
7
4
2. Find the maximal flow from node 1 to node 8 in the following network. Identify the associated minimal
cut.
3. Find the maximal flow from node 1 to node 7 in the following network. Identify the associated minimal
cut. Also write the associated linear programming problem.
4. Find the minimal spanning tree for the following network.
2000
2
1100
1300
5
2200
800
1000
4
1
780
6
1400
3
7
2600
1300
300
5. Find the shortest path from node 1 to every other node in the following network. Identify the shortest
path tree obtained.
dij
6. Assume that we want to construct a tin can with maximum volume using a 20 by 30 Aluminum sheet,
Formulate the problem as a nonlinear programming with linear constraints.
7. We want to cover the surface of a ball with radius 7 cm with an aluminum foil which its standard width
is 10 cm. Write a mathematical programming problem in a manner that the above goal done by
minimum length of aluminum foil.
8. How can we make a square and a circle with maximum total area by a thread with length L?
9. Contemporary Issues Report must be 8-10 pages containing (3 bonus points)
a. Cover Page
b. Table of Content
c.
Introduction (definition of contemporary issues and selected subjects)
d. Contemporary Issues List (at least 5 new subjects)
e. Selected Subject Explain with a Conclusion (at least three hand writing pages).
f.
References