Integer Programming
Chapter 5
Q13.
Solution
Let
X
1
,
X
2
= numbers of salespeople assign region 1 and region 2 respectively
Y
1
= 0 if no sales office in region 1, and 1 if sales office opened in region 1
Max
z
= 85000
X
1
+ 60000
X
2
 18000 Y
1
s.t. :
X
1
+
X
2
≤
10
10000X
1
+ 7000
X
2
≤
72000
X
1
 10 Y
1
≤
0
X
i
≥
0
X
i
= integer
Y
1
= 0 or 1
Q15
Solution
Let
F
1
,
F
2
,
F
3
,
F
4
,
F
5
,
F
6
= number of employees working at Midnight, 4:00am, 8:00am, Noon,
4:00pm and 8:00pm respectively
Min
z
=
F
1
+
F
2
+
F
3
+
F
4
+
F
5
+
F
6
s.t. :
F
1
+
F
6
≥
90
F
1
+
F
2
≥
215
F
2
+
F
3
≥
250
F
3
+ F
4
≥
65
F
4
+ F
5
≥
300
F
5
+ F
6
≥
125
F
i
≥
0
F
i
=
integer
Q18.
Solution
Let
X
1
,
X
2
,
X
3
= number of denim jeans, CD players and Compact discs respectively
Max
z
= 90
X
1
+ 150
X
2
+ 30
X
3
s.t. :
2
X
1
+ 3
X
2
+
X
3
≤
5
X
i
≥
0
X
i
= integer
Q19.
Solution
Let
X
1
,
X
2
,
X
3
= number of salespeople allocate to Alsace, Bourgogne, and ÎledeFrance
respectively
Max
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 Spring '10
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 Compact Disc, Denim, Nikon Fmount, Giorgetto Giugiaro, Solution Let X1

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