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 $1$:$1).$

After learning the value of flexibility from an operations lecture, TG$$s manager decides to cross$-$ train the workers in Molding Workshop A and Molding Workshop B$,$ so that they are capable of molding both basic and funky items. It still takes $3$ minutes for a worker to process a basic item and $5$ minutes for a worker to

process a funky item. Below is the new process diagram of TG$.$

c$)$ What are the capacity $($in items per hour$)$ and implied utilization of the Molding Workshop when the

molding workers are cross$-$trained?

d$)$ When assembly workers are cross$-$trained $($but molding workers are not cross$-$trained$),$ which

workstation is the bottleneck? What is the capacity of Trojan Gadgets in items per hour?