hw7_sol - Figure 1 From the left to the right are shown the...

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Figure 1: From the left to the right are shown the basic feasible solutions for Exercise 1 parts(a)-(c), respectively. Homework 7 March 17, 2009 Exercise 1, page 211 . Use only northwest-corner method to generate a basic feasible solution. Solution : The rows of the table correspond to resource areas i = 1 , 2 , 3 and the columns correspond to demand areas j = 1 , 2 , 3. Let x ij denote the allocation of resources from source i to demand area j . The models are balanced, so we can immediately apply the northwest-corner method. Figure 1 illustrates the resulting basic feasible solutions. (a) We set x 11 = 5 so that the demand at area 1 is fulfilled, and we carry 1 unit to area 2, so we have x 12 = 1. The resources of source 1 have been all assigned (6 units). Now we start by using resource at area 2, and we assign 4 units to satisfy the demand at center 2, which corresponds to x 22 = 4. At this point we have 3 units left at resource 2, and we assign them to demand area 3, i.e., x 23 = 3. At this point the resources at area 2 are depleted. We now go to use the resources at area 3. We assign all 7 units to demand area 3, i.e., x 33 = 7, and we are done. (b) We set x 11 = 7 so that all resources at 1 are assigned. We move to resource 2. We assign 3 units to demand center 1, so that x 21 = 3 . The remaining 9 units at resource 2 are all assigned to demand center 2, i.e., x 22 = 9. At this point the resources at area 2 are depleted. 1
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We now go to use the resources at area 3. We assign 1 unit to demand area 2, i.e., x 32 = 1, so that the demand at area 2 is satisfied. We assign the remaining 10 units of resource at area 3 to the demand center 3, i.e., x 33 = 10 , and we are done. (c) We set x 11 = 9 and we give the remaining 3 units to demand center 2, x 12 = 3, so that all resources at 1 are assigned. We move to resource 2. We assign 7 units to demand center 2, so that x 22 = 7 . The remaining 7 units at resource 2 are all assigned to demand center 3, i.e.,
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hw7_sol - Figure 1 From the left to the right are shown the...

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