Scott and Associates, Inc., is an accounting firm that has three new clients. Project leaders will be assigned to the three clients. Based on the different backgrounds and experiences of the leaders, the various leader$-$client assignments differ in terms of projected completion times. The possible assignments and the estimated completion times in days are as follows.

Project Leader Client

$123$

Jackson$1101632$

Ellis$2142240$

Smith$3222434$

$($a$)$

Develop a network representation of this problem. $($Submit a file with a maximum size of $1$ MB$.)$

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$($b$)$

Formulate the problem as a linear program. $($Express your answers in the form xij where xij represents the completion time from leader i to client j$.)$

Min

s$.$t$.$

Jackson

Ellis

Smith

Client $1$

Client $2$

Client $3$

xij $>=0$ for all i$,$ j$.$

Solve.

Relationship Assignment Time $($days$)$

x$11$

x$12$

x$13$

x$21$

x$22$

x$23$

x$31$

x$32$

x$33$

What is the total time required $($in days$)?$

days