Topic $5-$ Linear Programming: Distril

a$.$ Choose the correct network representation of the problem.

$($i$)$

$($ii$)$

$180$

$180$

$75$

$100$

$85$

$130$

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$z$

Topic $5-$ Linear Programming: Distril what is the total billing?

Let $x_{ij}=$ number of hours from consultant i assigned to client $j.$

$\backslash$table$[[,$Hours Assigned,$],[$Avery$-$Client A$,,$Billing$],[$Avery$-$Client B$,,],[$Avery$-$Client C$,,],[$Avery$-$Client D$,,],[$Baker$-$Client A$,,],[$Baker$-$Client B$,,]]$

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Topic $5-$ Linear Programming: Distril

$\backslash$table$[[,$Heurs Assigned$],[$Avery$-$Client A$,],[$Avery$-$Client B$,],[$Avery$-$Client C$,],[$Baker$-$Client A$,],[$Baker$-$Client B$,],[$Baker$-$Client C$,],[$Baker$-$Client D$,],[$Campbell$-$Client A$,],[$Campbell$-$Client B$,],[$Campbell$-$Client C$,],[$Campbell$-$Client D$,],[$Total Billing,$]]$

$\backslash$table$[[,$Hours Assigned,$],[$Avery$-$Client A$,,$Billing$],[$Avery$-$Client B$,,],[$Avery$-$Client C$,,]]$

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Topic $5-$ Linear Programming: Distril

$\backslash$table$[[$Campbell$-$Client B$,,],[$Campbell$-$Client C$,,],[$Campbell$-$Client D$,,],[$Total Billing,,$]]$

$\backslash$table$[[,$Hours Assigned,$],[$Avery$-$Client A$,,],[$Avery$-$Client B$,,],[$Avery$-$Client C$,,],[$Avery$-$Client D$,,],[$Baker$-$Client A$,,],[$Baker$-$Client B$,,],[$Baker$-$Client C$,,],[$Baker$-$Client D$,,],[$Campbell$-$Client A$,,],[$Campbell$-$Client B$,,],[$Campbell$-$Client C$,,],[$Campbell$-$Client D$,,],[$Total Billing,,$]]$

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Problem $10-05$ company has four clients with projects in process. The estimated hourly requirements for each of the clients over the four$-$week period are as follows:

$\backslash$table$[[$Client$,$Hours$],[$A$,180],[$B$,75],[$C$,100],[$D$,85]]$

Hourly rates vary for the consultant$-$client combination and are based on several factors, including project type and the consultant's experience. The rates $($dollars per hour$)$ for each consultant$-$client combination are as follows:

$\backslash$table$[[,$Client$],[$Consultant$,$A$,$B$,$C$,$D$],[$Avery$,100,125,115,100],[$Baker$,120,135,115,120],[$Campbell$,155,150,140,130]]$

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