$16.$ A construction company has just started the plumbing operation of five building projects $($P$1-$P$5)$ and requires $\backslash ($ X $\backslash )$ type and $\backslash ($ Y $\backslash )$ type skill workers. X type workers are outsourced from $3$ companies $(\backslash (\backslash$mathrm$\{$X$\}1,\backslash$mathrm$\{$X$\}2\backslash )$ and X $3)$ whereas Y type workers are outsourced from $4$ companies $($Y$1,$ Y$2,$ Y$3,$ and Y$4).$ Each company has been assigned a unique effective index per worker based on past performances as shown in the following table. Develop labor assignment plan for the construction company with the objective of maximizing the total effective index.

Labor requirement for each project from each worker category