The below question is in linear programming. I will leave a thumbs up for a good
ID: 3004409 • Letter: T
Question
The below question is in linear programming. I will leave a thumbs up for a good explanation. Thank you!
A political candidate wants to make a mass mailing to counteract some nasty remarks made recently by her opponent. Our candidate has identified five mailing lists that contain names and addresses of voters she might like to reach. Each list can be purchased for a price. Partial lists are not for sale. The number of names on each list in each of four professional categories are listed below along with the desired number of names to reach in each category and the price of each list. Find the subset of lists that will give the required coverage at minimum cost.
List
Law
HealthCare
Bus. Execs.
Academe
Price
1
28
4
7
2
$41,000
2
9
29
11
3
$52,000
3
6
3
34
18
$61,000
4
2
4
6
20
$32,000
5
8
9
12
14
43,000
Desired coverage
20
18
22
20
List
Law
HealthCare
Bus. Execs.
Academe
Price
1
28
4
7
2
$41,000
2
9
29
11
3
$52,000
3
6
3
34
18
$61,000
4
2
4
6
20
$32,000
5
8
9
12
14
43,000
Desired coverage
20
18
22
20
Explanation / Answer
The required number
Z = 20w + 18x + 22y + 20z
We need to select the minimum number of lists that satisfy the Z with the given critera
28w + 4x + 7y + 2z = 41000
9w + 29x + 11y + 3z = 52000
6w + 3x + 34y + 18z = 61000
2w + 4x + 6y + 20z = 32000
8w + 9x + 12y + 20z = 43000
Reason:
1 List can't satisfy the criteria
2 List can't satisfy all the criteria
make the pair of three lists ,there will be 10 pairs
L1L2L3, L1L2L4,L1L2L5,L1L3L4,L1L3L5,L2L3L4,L2L3L5,L3L4L5,L1L4L5
The minimum will be otained when we select List1, List 2 and List 4
The minimum cost will be 41000 + 52000 + 32000 = 125000$
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