Step 1 Row Minimization

Question:- Five swimmers are eligible to compete in a relay team which is to consist of four swimmers swimming four different swimming styles; back stroke, breast stroke, free style and butterfly. The time taken for the five swimmers – Anand, Bhaskar, Chandru, Dorai and Eswar - to cover a distance of 100 meters in various swimming styles are given below in minutes and seconds. Anand swims the back stroke in 1:09, the breast stroke in 1:15 and has never competed in the free style or butterfly. Bhaskar is a free style specialist averaging 1:01 for the 100 meters but can also swim the breast stroke in 1:16 and butterfly in 1:20. Chandru swims all types – back stroke in 1:10, butterfly 1:12, free style 1:05 and breast stroke 1:20. Dorai swims only the butterfly 1:11, while Eswar swims the back stroke 1:20, the breast stroke 1:16, the free style 1:06 and the butterfly1:10. Which swimmers should be assigned to which swimming style? Who will not be in the relay? Back Breast stroke stroke Anand 1:09 1:15 Bhaskar 1:16 Chandru 1:10 1:20 Dorai Eswar 1:20 1:16 Step 1 Row minimization

Free style 1:01 1:05 1:06

Butterfly Dummy1 1:20 1:12 1:11 1:10

0 0 0 0 0

1:09

1:15

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0

-

1:16

1:01

1:20

0

1:10

1:20

1:05

1:12

0

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-

1:11

0

1:20

1:16

1:06

1:10

0

Step 2 Column minimization 0 M 0:01 M 0:11

0 0:01 0:05 M 0:01

M 0 0:04 M 0:05

M 0:10 0:02 0:01 0

0 0 0 0 0

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M

0

M

0:01

0

0:10

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0:01

0:05

0:04

0:02

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M

M

0:01

0



0:11

0:01

0:05

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M

0:01

M

0:01

0

0:10

0:01

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0:04

0:03

0:01

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M

0

0

0:11

0:01

0:05

0

0:01

Assignment Anand – Breast stroke Bhaskar – Free style Chandru – Back stroke Dorai – Dummy Eswar – Butterfly

Dorai will be not in the relay.