Problem $10-17$

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:

Choose the correct network representation of this problem.

$($i$)($ii$)$

$($iii$)($iv$)$

Formulate the problem as a linear program, and solve. What is the total time required?

Min fill in the blank $2$

x$11+$ fill in the blank $3$

x$12+$ fill in the blank $4$

x$13+$ fill in the blank $5$

x$21+$ fill in the blank $6$

x$22+$ fill in the blank $7$

x$23+$ fill in the blank $8$

x$31+$ fill in the blank $9$

x$32+$ fill in the blank $10$

x$33$

s$.$t$.$

fill in the blank $11$

x$11+$ fill in the blank $12$

x$12+$ fill in the blank $13$

x$13<=$ fill in the blank $14$

fill in the blank $15$

x$21+$ fill in the blank $16$

x$22+$ fill in the blank $17$

x$23<=$ fill in the blank $18$

fill in the blank $19$

x$31+$ fill in the blank $20$

x$32+$ fill in the blank $21$

x$33<=$ fill in the blank $22$

fill in the blank $23$

x$11+$ fill in the blank $24$

x$21+$ fill in the blank $25$

x$31=$ fill in the blank $26$

fill in the blank $27$

x$12+$ fill in the blank $28$

x$22+$ fill in the blank $29$

x$32=$ fill in the blank $30$

fill in the blank $31$

x$13+$ fill in the blank $32$

x$23+$ fill in the blank $33$

x$33=$ fill in the blank $34$

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

x$11=$ fill in the blank $35$

x$12=$ fill in the blank $36$

x$13=$ fill in the blank $37$

x$21=$ fill in the blank $38$

x$22=$ fill in the blank $39$

x$23=$ fill in the blank $40$

x$31=$ fill in the blank $41$

x$32=$ fill in the blank $42$

x$33=$ fill in the blank $43$

Total time required $=$ fill in the blank $44$