Before a design is approved, it must be reviewed $($perhaps multiple times$)$ by each of three categories of engineers $($one civil, one mechanical, and one industrial$).$ It takes a civil engineer an average of $2$ hours to review a design, while mechanical and industrial engineers spend an average of $3$ and $2$ hours on such reviews, respectively. Designs are often reviewed more than once: on average, each design is reviewed by a civil, mechanical, and industrial engineer $2,2,$ and $3$ times, respectively. What is the bottleneck capacity $($in units of designs per hour$)$ of an organization $($with respect to reviewing designs for approval$)$ given that it has $4,6,$ and $4$ civil, mechanical, and industrial engineers $($respectively$)$ available to review designs at any given time?