On average. the R&D department generates about $15$ new toy ideas a week. To go from idea to approved product, the idea must go through $5$sequent aracuvres.In initial screening. a staff member spends $2$ hours considering the idea. In mock$-$up the idea is sent to one of man suppliers to produce a physical mock$-$up of the tov. There is essentiall unlimited capacitv at this activity. but it takes $4$ days to get the mockup built even though multiple mockups can be built simultaneously. In safetv testing, each idea requires $2$ days from a staff member to have the idea checked for safety. In focus groups, each idea requires $3$ hours from a staff member to have the idea test marketed. Finally, the management team meets for $4$ hours per idea to decide if the toy should be added to its line of products sold to customers.For example, there are $7$ staff members that work in the safety activity. In each activity, each idea is processed by only one staff member: for example, once one of the $7$ staff members starts working on an idea in the safety activity, the idea completes that activity in $2$ days $($and either exits or moves to the focus group activity$).$ Everyone works $8$ hours per day, $5$ days a week.a$)$ On average, how many ideas are in the mock$-$up activity?b$)$ Implied utilization at each activity is defined as demand divided by capacity $($where we recall that the demand at each activity is defined as the activity's input flow rate if the capacity at each of the activities was infinite$).$ Which activity has the highest implied utilization $($as a $\%)?$