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Linear Programming Applications in Marketing, Finance and Operations Management
Chapter 4 Homework Solutions
Problem 1, 2a, 3, 4abc, 8, 11, 14ab, 17abc, 18
1.
a.
Let
T
= number of television spot advertisements
R
= number of radio advertisements
N
= number of newspaper advertisements
Max
100,000
T
+
18,000
R
+
40,000
N
s.t.
2,000
T
+
300
R
+
600
N
≤
18,200
Budget
T
≤
10
Max TV
R
≤
20
Max Radio
N
≤
10
Max News
0.5
T
+
0.5
R

0.5
N
≤
0
Max 50% Radio
0.9
T

0.1
R

0.1
N
≥
0
Min 10% TV
T
,
R
,
N
,
≥
0
Budget $
Solution:
T
= 4
$8,000
R
= 14
4,200
N
= 10
6,000
$18,200
Audience = 1,052,000.
b.
The dual price for the budget constraint is 51.30.
Thus, a $100 increase in budget should provide an
increase in audience coverage of approximately 5,130.
The righthandside range for the budget
constraint will show this interpretation is correct.
2.
a.
Let
x
1
= units of product 1 produced
x
2
= units of product 2 produced
Max
30
x
1
+
15
x
2
s.t.
x
1
+
0.35
x
2
≤
100
Dept. A
0.30
x
1
+
0.20
x
2
≤
36
Dept. B
0.20
x
1
+
0.50
x
2
≤
50
Dept. C
x
1
,
x
2
≥
0
Solution:
x
1
= 77.89,
x
2
= 63.16
Profit = 3284.21
3.
x
1
= $ automobile loans
x
2
= $ furniture loans
x
3
= $ other secured loans
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x
4
= $ signature loans
x
5
= $ "risk free" securities
Max
0.08
x
1
+
0.10
x
2
+
0.11
x
3
+
0.12
x
4
+
0.09
x
5
s.t.
x
5
≤
600,000
[1]
x
4
≤
0.10(
x
1
+
x
2
+
x
3
+
x
4
)
or
0.10
x
1

0.10
x
2

0.10
x
3
+
0.90
x
4
≤
0
[2]
x
2
+
x
3
≤
x
1
or

x
1
+
x
2
+
x
3
≤
0
[3]
x
3
+
x
4
≤
x
5
or
+
x
3
+
x
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 Spring '10
 KUMAR

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