Meghan has collected some information, using the Friendly Seas I ship, for you to analyze and to make a recommendation to her. The Friendly Seas I carries $1,250$ passengers $(1,100$ are processed through normal registration with the remaining $150$ processed as VIP's$).$ A diagram of the process is available at Embarkation Process. Currently, the company has $12$ staff members processing regular registrations and $4$ staff members processing VIP's. On average it takes $3$ minutes to process a regular guest and $4$ minutes to process a VIP guest. Typically the embarkation process requires $6$ hours and runs from $12$ noon till $6$:$00$ p$.$m$.$ In addition to the registration procedure, guests also pass through a photographers section and a security check station.

Meghan's figures indicate that that on average, about $550$ guests arrive between noon and $1$:$00$ p$.$m$.,300$ more guests from $1$:$00$ to $2$:$00$ p$.$m$.,200$ guests between $2$:$00$ and $3$:$00$ p$.$m$.,100$ guests arrive between $3$:$00$ and $4$:$00$ p$.$m$.,70$ guests between $4$:$00$ and $5$:$00$ p$.$m$.,$ and the remaining $30$ guests arrive after $5$:$00$ p$.$m$.$ A portion of these guests $(150)$ are VIP's. Data shows that $50$ VIP's arrive between noon and $1$:$00$ p$.$m$.,40$ more between $1$:$00$ to $2$:$00$ p$.$m$.,30$ more between $2$:$00$ to $3$:$00$ p$.$m$.,20$ more between $3$:$00$ to $4$:$00$ p$.$m$.$ and the remaining $10$ between $4$:$00$ and $5$:$00$ p$.$m$.$