Question $1.(30$ Points$)$

A bookstore receives shipments of new books every day. The process of receiving and stocking new books

includes three activities with the following sequence:

$1-$ Unpacking and inspecting the books $($done by worker W$1),$ which takes $10$ minutes per box.

$2-$ Scanning the books into the bookstore system $($done by worker W$2),$ which takes $5$ minutes per

box.

$3-$ Stocking the books on the shelves $($done by worker W$3),$ which takes $15$ minutes per box.

Assuming that the bookstore receives $24$ boxes of new books every day and the workers work $8$ hours per

day, answer the following questions:

$($a$)$ What is the input rate of boxes per hour?

$($b$)$ What is the capacity rate of the process per hour? Show all your work and justify your answer, and do

not forget the units.

$($c$)$ What is the throughput rate of the process per hour? What does throughput rate mean in this context?

Explain using the definition, context and the number you have obtained.

$($d$)$ What is the utilization of each of the resources if the process runs for $8$ hours a day and $24$ boxes of

books are received each day? Show details of your work, justify your answers, and include all the units.