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# HW4_Sol - Telcom 2110 Network Design Homework#4 Spring 2010...

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Telcom 2110 Network Design Homework #4 Spring 2010 1. Consider linear programming problem below (a) Draw the feasible solution space (b) Find the optimal solution graphically Maximize Z = 5 X 1 + 4 X 2 Subject to 4X 1 + 2 X 2 < = 25 X 2 < = 4 X 1 => 0 X 2 => 0 The feasible region is the red shaded area. The optimal solution X1 = 4.25, X2 = 4 which gives the maximum objective value Z = 37.5

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2. Consider the four node network shown below, (a) State clearly a set of eligible distinct routes between node 1 and node 2 (either by drawings or text) (b) Define decision variables used in the arc path maximum flow LP formulation (c) Write the linear program formulation to find the maximum flow from node 1 to node 4 using the end-to-end arc path approach. The capacity of each link is given in the table below. In the table the links are numbered one through six with the nodes they connect show in parentheses. (d) Using a linear program solver (e.g., Excel, AMPL, Matlab, etc.) solve the problem and determine the amount of flow on each path. a) There are five possible routes from node 1 to node 2 Route 1 1-2 ( link between node 1 and node 2) Route 2 1-4-2
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HW4_Sol - Telcom 2110 Network Design Homework#4 Spring 2010...

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