The below question is in linear programming I will leave a t

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

Solution

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$