A computer contains 8,000 diodes. When one diode fails, it is replaced. The cost of replacing it individually is Kshs. 40 only. If all the diodes are replaced at the same time, the cost per diode would reduce to Kshs.28. The percentage of surviving diodes, s (t) at the end of the month t is
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t
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0
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1
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2
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3
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4
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5
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6
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S (t)
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100
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90
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84
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75
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40
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18
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0
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a. What is the best replacement plan assuming that individual failures before fixed replacement period are done at the end of the period they fail?
b. Evaluate the following using the Lagrange multiplier approach
Max P=X2+Y2
S.t X+Y≥11
2X+Y≥17
X, Y≥0
A salesman located in city 1 decided to travel to a city 10. He knew the bus fare for alternative routes from 1 to 10. He then drew a highway network map as shown in the diagram below.
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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1
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400
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600
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300
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|
|
|
|
|
|
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2
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|
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|
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700
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1000
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500
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|
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3
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|
|
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300
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800
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400
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|
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4
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|
|
|
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600
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800
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500
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|
|
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5
|
|
|
|
|
|
|
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400
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800
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|
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6
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|
|
|
|
|
|
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300
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700
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|
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7
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|
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|
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800
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400
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8
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|
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700
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9
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|
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900
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The bus fare between cities 1-2 is the same as 2-1 etc and that the black spaces indicate that the routes are infeasible
Required
As an application to dynamic programming algorithm,
a. Draw a network diagram to represent the movement from origin (node 1) to destination or sink (node 10) clearly indicating the stages and nodes
b. Determine the path and hence the minimum bus fare for the problem