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 northwestcorner 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 northwestcorner 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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View Full DocumentWe 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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 Spring '09
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