Решение задачи оптимизации производства методом динамического программирования, страница 2

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S

x

S-x

φ4 (x)

W5 (S - x)

φ4(x) + W5(S-x)

x4 (S)

W4 (S)

1

1

0

0,49000

0,00000

0,49000

0

1,44375

0

1

0,00000

1,44375

1,44375

2

2

0

0,85750

0,00000

0,85750

1

1,93375

1

1

0,49000

1,44375

1,93375

0

2

0,00000

1,70625

1,70625

3

3

0

1,83750

0,00000

1,83750

2

2,30125

2

1

0,85750

1,44375

2,30125

1

2

0,49000

1,70625

2,19625

0

3

0,00000

1,96875

1,96875

4

4

0

1,96000

0,00000

1,96000

3

3,28125

3

1

1,83750

1,44375

3,28125

2

2

0,85750

1,70625

2,56375

1

3

0,49000

1,96875

2,45875

0

4

0,00000

2,10000

2,10000

5

5

0

2,08250

0,00000

2,08250

3

3,54375

4

1

1,96000

1,44375

3,40375

3

2

1,83750

1,70625

3,54375

2

3

0,85750

1,96875

2,82625

1

4

0,49000

2,10000

2,59000

0

5

0,00000

2,23125

2,23125

6

6

0

2,20500

0,00000

2,20500

3

3,80625

5

1

2,08250

1,44375

3,52625

4

2

1,96000

1,70625

3,66625

3

3

1,83750

1,96875

3,80625

2

4

0,85750

2,10000

2,95750

1

5

0,49000

2,23125

2,72125

0

6

0,00000

2,36250

2,36250

7

7

0

2,32750

0,00000

2,32750

3

3,93750

6

1

2,20500

1,44375

3,64875

5

2

2,08250

1,70625

3,78875

4

3

1,96000

1,96875

3,92875

3

4

1,83750

2,10000

3,93750

2

5

0,85750

2,23125

3,08875

1

6

0,49000

2,36250

2,85250

0

7

0,00000

2,49375

2,49375

8

8

0

2,32750

0,00000

2,32750

3

4,06875

7

1

2,32750

1,44375

3,77125

6

2

2,20500

1,70625

3,91125

5

3

2,08250

1,96875

4,05125

4

4

1,96000

2,10000

4,06000

3

5

1,83750

2,23125

4,06875

2

6

0,85750

2,36250

3,22000

1

7

0,49000

2,49375

2,98375

0

8

0,00000

2,62500

2,62500

9

9

0

2,32750

0,00000

2,32750

3

4,20000

8

1

2,32750

1,44375

3,77125

7

2

2,32750

1,70625

4,03375

6

3

2,20500

1,96875

4,17375

5

4

2,08250

2,10000

4,18250

4

5

1,96000

2,23125

4,19125

3

6

1,83750

2,36250

4,20000

2

7

0,85750

2,49375

3,35125

1

8

0,49000

2,62500

3,11500

0

9

0,00000

2,62500

2,62500

10

10

0

2,32750

0,00000

2,32750

3

4,33125

9

1

2,32750

1,44375

3,77125

8

2

2,32750

1,70625

4,03375

7

3

2,32750

1,96875

4,29625

6

4

2,20500

2,10000

4,30500

5

5

2,08250

2,23125

4,31375

4

6

1,96000

2,36250

4,32250

3

7

1,83750

2,49375

4,33125

2

8

0,85750

2,62500

3,48250

1

9

0,49000

2,62500

3,11500

0

10

0,00000

2,62500

2,62500

S

x

S-x

Φ3(x)

W4 (S - x)

Φ3(x) + W4(S-x)

x3 (S)

W3 (S)

1

1

0

0,79625

0,00000

0,79625

0

1,44375

0

1

0,00000

1,44375

1,44375

2

2

0

1,36500

0,00000

1,36500

1

2,24000

1

1

0,79625

1,44375

2,24000

0

2

0,00000

1,93375

1,93375

3

3

0

1,47875

0,00000

1,47875

2

2,80875

2

1

1,36500

1,44375

2,80875

1

2

0,79625

1,93375

2,73000

0

3

0,00000

2,30125

2,30125

4

4

0

1,70625

0,00000

1,70625

2

3,29875

3

1

1,47875

1,44375

2,92250

2

2

1,36500

1,93375

3,29875

1

3

0,79625

2,30125

3,09750

0

4

0,00000

3,28125

3,28125

5

5

0

1,93375

0,00000

1,93375

1

4,07750

4

1

1,70625

1,44375

3,15000

3

2

1,47875

1,93375

3,41250

2

3

1,36500

2,30125

3,66625

1

4

0,79625

3,28125

4,07750

0

5

0,00000

3,54375

3,54375

6

6

0

2,04750

0,00000

2,04750

2

4,64625

5

1

1,93375

1,44375

3,37750

4

2

1,70625

1,93375

3,64000

3

3

1,47875

2,30125

3,78000

2

4

1,36500

3,28125

4,64625

1

5

0,79625

3,54375

4,34000

0

6

0,00000

3,80625

3,80625

7

7

0

2,16125

0,00000

2,16125

2

4,90875

6

1

2,04750

1,44375

3,49125

5

2

1,93375

1,93375

3,86750

4

3

1,70625

2,30125

4,00750

3

4

1,47875

3,28125

4,76000

2

5

1,36500

3,54375

4,90875

1

6

0,79625

3,80625

4,60250

0

7

0,00000

3,93750

3,93750

8

8

0

2,27500

0,00000

2,27500

2

5,17125

7

1

2,16125

1,44375

3,60500

6

2

2,04750

1,93375

3,98125

5

3

1,93375

2,30125

4,23500

4

4

1,70625

3,28125

4,98750

3

5

1,47875

3,54375

5,02250

2

6

1,36500

3,80625

5,17125

1

7

0,79625

3,93750

4,73375

0

8

0,00000

4,06875

4,06875

9

9

0

2,27500

0,00000

2,27500

2

5,30250

8

1

2,27500

1,44375

3,71875

7

2

2,16125

1,93375

4,09500

6

3

2,04750

2,30125

4,34875

5

4

1,93375

3,28125

5,21500

4

5

1,70625

3,54375

5,25000

3

6

1,47875

3,80625

5,28500

2

7

1,36500

3,93750

5,30250

1

8

0,79625

4,06875

4,86500

0

9

0,00000

4,20000

4,20000

10

10

0

2,27500

0,00000

2,27500

4

5,51250

9

1

2,27500

1,44375

3,71875

8

2

2,27500

1,93375

4,20875

7

3

2,16125

2,30125

4,46250

6

4

2,04750

3,28125

5,32875

5

5

1,93375

3,54375

5,47750

4

6

1,70625

3,80625

5,51250

3

7

1,47875

3,93750

5,41625

2

8

1,36500

4,06875

5,43375

1

9

0,79625

4,20000

4,99625

0

10

0,00000

4,33125

4,33125

S

x

S-x

φ2 (x)

W3 (S - x)

φ2(x) + W3(S-x)

x2 (S)

W2 (S)

1

1

0

0,21000

0,00000

0,21000

0

1,44375

0

1

0,00000

1,44375

1,44375

2

2

0

0,63000

0,00000

0,63000

0

1,93375

1

1

0,21000

1,44375

1,65375

0

2

0,00000

1,93375

1,93375

3

3

0

1,36500

0,00000

1,36500

0

2,30125

2

1

0,63000

1,44375

2,07375

1

2

0,21000

1,93375

2,14375

0

3

0,00000

2,30125

2,30125

4

4

0

1,99500

0,00000

1,99500

0

3,28125

3

1

1,36500

1,44375

2,80875

2

2

0,63000

1,93375

2,56375

1

3

0,21000

2,30125

2,51125

0

4

0,00000

3,28125

3,28125

5

5

0

2,73000

0,00000

2,73000

0

3,54375

4

1

1,99500

1,44375

3,43875

3

2

1,36500

1,93375

3,29875

2

3

0,63000

2,30125

2,93125

1

4

0,21000

3,28125

3,49125

0

5

0,00000

3,54375

3,54375

6

6

0

3,15000

0,00000

3,15000

5

4,17375

5

1

2,73000

1,44375

4,17375

4

2

1,99500

1,93375

3,92875

3

3

1,36500

2,30125

3,66625

2

4

0,63000

3,28125

3,91125

1

5

0,21000

3,54375

3,75375

0

6

0,00000

3,80625

3,80625

7

7

0

3,78000

0,00000

3,78000

5

4,66375

6

1

3,15000

1,44375

4,59375

5

2

2,73000

1,93375

4,66375

4

3

1,99500

2,30125

4,29625

3

4

1,36500

3,28125

4,64625

2

5

0,63000

3,54375

4,17375

1

6

0,21000

3,80625

4,01625

0

7

0,00000

3,93750

3,93750

8

8

0

3,99000

0,00000

3,99000

4

5,27625

7

1

3,78000

1,44375

5,22375

6

2

3,15000

1,93375

5,08375

5

3

2,73000

2,30125

5,03125

4

4

1,99500

3,28125

5,27625

3

5

1,36500

3,54375

4,90875

2

6

0,63000

3,80625

4,43625

1

7

0,21000

3,93750

4,14750

0

8

0,00000

4,06875

4,06875

9

9

0

4,09500

0,00000

4,09500

5

6,01125

8

1

3,99000

1,44375

5,43375

7

2

3,78000

1,93375

5,71375

6

3

3,15000

2,30125

5,45125

5

4

2,73000

3,28125

6,01125

4

5

1,99500

3,54375

5,53875

3

6

1,36500

3,80625

5,17125

2

7

0,63000

3,93750

4,56750

1

8

0,21000

4,06875

4,27875

0

9

0,00000

4,20000

4,20000

10

10

0

4,20000

0,00000

4,20000

5

6,80750

9

1

4,09500

1,44375

5,53875

8

2

3,99000

2,24000

6,23000

7

3

3,78000

2,80875

6,58875

6

4

3,15000

3,29875

6,44875

5

5

2,73000

4,07750

6,80750

4

6

1,99500

4,64625

6,64125

3

7

1,36500

4,90875

6,27375

2

8

0,63000

5,17125

5,80125

1

9

0,21000

5,30250

5,51250

0

10

0,00000

5,51250

5,51250

S

x

S-x

φ1 (x)

W2 (S - x)

φ1(x) + W2(S-x)

x1 (S)

W1 (S)

10

10

0

3,46500

0,00000

3,46500

0

6,80750

9

1

3,36875

1,44375

4,81250

8

2

3,27250

1,93375

5,20625

7

3

2,88750

2,30125

5,18875

6

4

2,79125

3,28125

6,07250

5

5

2,50250

3,54375

6,04625

4

6

2,02125

4,17375

6,19500

3

7

1,44375

4,66375

6,10750

2

8

1,05875

5,27625

6,33500

1

9

0,57750

6,01125

6,58875

0

10

0,00000

6,80750

6,80750