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IEOR 162 LINEAR PROGRAMMING FALL 04
HOMEWORK 4 SOLUTIONS
3.5.2.
Let x
1
= employees starting at midnight
x
2
= employees starting at 4 AM
x
3
= employees starting at 8 AM
x
4
= employees starting at noon
x
5
= employees starting at 4 PM
x
6
= employees starting at 8 PM
Then a correct formulation is
min z
=
x
1
+ x
2
+ x
3
+ x
4
+ x
5
+ x
6
s.t.
x
1
+ x
6
≥
8
x
1
+ x
2
≥
7
x
2
+ x
3
≥
6
x
3
+ x
4
≥
6
x
4
+ x
5
≥
5
x
5
+ x
6
≥
4
x
1
, x
2
, x
3
, x
4
, x
5
, x
6
≥
0
3.8.5.
We assume the following order of events ensues each month.
a. Shortterm loan and interest on short and longterm loans
are paid. We assume first interest payments on the January short
term and longterm loan are made at beginning of February.
b. New shortterm loan (or Longterm Loan) is received
c. Month's cash flow is accounted for
d. Interest on balance is received
All variables are in thousands of dollars
Let Bt = Month t balance after month t's cash flow is accounted
for. t =1, 2, .
..,12
LT = Longterm Loan
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 Fall '07
 Zhang

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