Please write the steps that led you to your answer in detail. Clear and logical justification

must be given for either full or partial credit.

Q$1.$ The below diagram shows the demand rate at a urgent care clinic. From $6$:$00$ am to

$12$:$00$ pm$,$ the demand rate is $5$ patients per hour. From $12$:$00$ pm to $6$:$00$ pm$,$ the demand

rate is $10$ patients per hour. The demand rate is zero at other times. The clinic can treat

patients at a rate of $5$ patients per hour. Assume patients wait at the clinic until they are

treated.

$($a$)$ What is the inventory$-$changing rate between $6$:$00$ am and $12$:$00$ pm$?$ What is the

inventory level $($i$.$e$.,$ number of patients$)$ at $12$:$00$ pm$?$