$[$Q$5$: Process Management$]($Spring $2021$ Final Exam Problem$)$ Gopher Tax is a family$-$owned small

business that services two types of customers: personal tax and business tax customers. The firm's process

flow is as follows.

Reception: There is $1$ receptionist, who needs to spend $8$ minutes with every customer $($regardless

of personal or business$)$ to fill out some requisite information. Afterwards, $75\%$ of customers will

move on to see their consultants in Department P for personal taxes, and $25\%$ of customers go to

Department B for business taxes.

Department $P$ and John: Each personal tax customer needs to meet with a tax consultant in

Department $P$ for $60$ minutes. Department $P$ has $4$ consultants. After a consultant finishes

processing a customer, John checks$/$corrects$/$makes changes to the consultants. This takes $20$

minutes, at the end of which the customer exits the system.

Department B and Emily: Each business tax customer needs to meet with a tax consultant in

Department B for $120$ minutes. Department B has $2$ consultants. After a consultant finishes

processing a customer, Emily checks$/$corrects$/$makes changes to the consultants. This takes $65$

minutes, at the end of which the customer exits the system.

During the tax season, the daily demand on average is $40$ customers. Everyone in Gopher Tax works $8$

hours per day. $[$Hint: each worker's daily capacity is $8$ hours $=480$ minutes.$]$

a$)$ Find the implied utilization for Department P$.($Please leave two decimal points.$)$