Quantitative Methods - StudentOfFortune.com

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$7.00 Quantitative Methods

From Mathematics: General-Mathematics , Mathematics: General-Mathematics
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Due on Jun. 07, 2009
Asked on Jun 05, 2009 at 6:24:50PM

Q:
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The state is considering the establishment of job training centers at four centers
because of the economy. The following table indicates the cost at each site and whether
the site can provide adequate service to each of the state's five service regions.
The goal is to provide a minimum cost collection of sites that can service all five
regions if this is possible.
Site
Region 1 2 3 4
Northwest x x
Southwest x x x
Capital x x x
Northeast x x
Southeast x x
Cost (000) 200 40 55 75

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$10.00 Formulating a Modeling Problem

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Posted on Jun 05, 2009 at 6:29:16PM

A:
Preview: ... s are 0-1 valued, we know that 200*X1 is the cost of site 1. If it is selected then X1 = 1, so the cost is 200, if it isn't then X1 = 0, so the cost is 0. Then all the fixed costs added up are 200*X1 + 40*X2 + 50*X3 + 75*X4 Now let's look at the training costs. We'll address these in each region as well. For the Northwest region the cost for the clients for site 1 is the number of clients served times the cost / client . We can encode this as 10 * 4100 * X1 /(X1 + X2) Let's break this down. The 10 is the cost / client. The 4100 is the # of clients, so 10*4100 is the cost. Now X1/(X1 + X2) is either 0, 1, or 1/2 depending on whether X1 = 0, or X1 = 1 and X2 = 0, or X1 = X2 = 1. That fraction is encoding what percentage of the clients in the North ...

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