Evan Cassimy
MGMT 651
1/26/2020
Professor Avijit Sarkar
Homework 3
1.
(20 points) Chapter 4 Problem 1*
Part A
Z = 100,000x
1
+ 18,000x
2
+ 40,000x
3
Budget Constraints:
2,000x
1
+ 300x
2
+ 600x
3
Minimum number of TV ads:
x
1
>
.10(x
1
+ x
2
+ x
3
)
.10x
2
+ .10x
3
+ - .90x
1
<
0
Maximum number of Radio ads:
x
2
<
.50(x
1
+ x
2
+ x
3
)
.50x
1
- .50x
2
+ .50x
3
>
0
Maximum number of TV ads:
x
1
<
10
Maximum number of radio ads:
x
2
<
20
Maximum number of newspaper ads:
X
3
<
10
Non-negativity constraints:
x
1
>
0
x
2
>
0
x
3
>
0
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applicable.
If you submit your homework as an MS-Excel document, make sure that it is properly
formatted to 8.5x11 page size!!
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Number of tv ads to be run
=
4
Number of radio ads to be run
=
14
Number of newspaper ads to be run
=
10
Allocated tv ad budget
=
$8,000
Allocated radio ad budget
=
$4,200
Allocated newspaper budget
=
$6,000
Total audience reacehd
=
1,052,000
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applicable.
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Part B
Z = 100,000x
1
+ 18,000x
2
+ 40,000x
3
Budget Constraints:
2,000x
1
+ 300x
2
+ 600x
3
<
18,300
Minimum number of TV ads:
x
1
>
.10(x
1
+ x
2
+ x
3
)
.10x
2
+ .10x
3
+ - 0.90x
1
<
0
Maximum number of Radio ads:
x
2
<
.50(x
1
+ x
2
+ x
3
)
.50x
1
- .50x
2
+ .50x
3
>
0
Maximum number of TV ads:
x
1
<
10
Maximum number of radio ads:
x
2
<
20
Maximum number of newspaper ads:
X
3
<
10
Non-negativity constraints:
x
1
>
0
x
2
>
0
x
3
>
0
Total audience reached
=
1,057,130
Audience contact increase
=
5,130
when an extra
$100
is allocated to the promotional budget.
2.
(15 points) Chapter 4 Problem 8.
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Consider
X
1
= number of officers beginning work from 8:00 AM – Noon
X
2
= number of officers beginning work from Noon – 4:00 PM
X
3
= number of officers beginning work from 4:00 PM – 8:00 PM
X
4
= number of officers beginning work from 8:00 – Midnight
X
5
= number of officers beginning work from Midnight – 4:00 AM
X
6
= number of officers beginning work from 4:00 AM – 8:00 AM
Objective function
Minimize Z = X
1
+ X
2
+ X
3
+ X
4
+ X
5
+ X
6
Subject to constraints
X
6
+ X
1
>
5
X
1
+ X
2
>
6
X
2
+ X
3
>
10
X
3
+ X
4
>
7
X
4
+ X
5
>
4
X
5
+ X
6
>
6
Restriction Variable
X
1
, X
2
, X
3
, X
4
, X
5
, X
6
>
0
Submit your homework as one single attachment. Include POM-QM input and output screenshots wherever
applicable.
If you submit your homework as an MS-Excel document, make sure that it is properly
formatted to 8.5x11 page size!!
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of
11