$[$Q$3$: Process Management$]$ Trojan Gadgets $($TG$)$ makes two products$$basic and funky. Molding

Workshop A processes basic items only; there is $1$ worker in Molding Workshop A$,$ and the worker can

process a basic item in $3$ minutes. Molding Workshop B processes funky items only; there are $2$ workers

in Molding Workshop B$,$ and each worker can process a funky item in $5$ minutes. Assembly Workshop C

has $3$ workers and assembles basic items only; it takes $4$ minutes for a worker to assemble a basic item.

Assembly Workshop D has $4$ workers and assembles funky items only; it takes $6$ minutes for a worker to

assemble a funky item. In the Packing Workshop, there is one packing machine that can pack an item in $1$

minute, regardless of the type of the product. The demand is $20$ pairs of basic items and funky items every

hour $($that is$,20$ items$/$hour for basic items and $20$ items$/$hour for funky items, the demand ratio is $1$:$1).$

a$)$ What are the capacities $($in items per hour$)$ and implied utilization of each workshop?

b$)$ Which workstation is the bottleneck? What is the capacity of Trojan Gadgets in items per hour?