$1.$ ?In the process shown below, $125$ ?applicants arrive at the registration step every day. Each applicant gos through registration in step $1$ ?which takes $15$ ?minutes in average. There is a buffer before entering step $2,$ ?and the average duration of waiting in that buffer is $15$ ?minutes.

At step $2,$ ?there is a assessment to specify where each applicant must go next, and depending on the findings of that assessment, usually $50\%$ ?of them are directed to step $3,$ ?which takes $10$ ?minutes in average for each applicant, while the rest of the applicants are directed to step $4$ ?which takes $30$ ?minutes in average. Once each applicant goes through the respective step $(3$ ?or $4),$ ?they exit this process. Please answer the following questions accordingly. start $1.$ ?registration, wait, $2.$ ?assessment $3.$ ?case A $4.$ ?case B $,$ ?end. Note:

$1)$ ?Consider each day as $8$ ?hours.

$2)$ ?Start and end points as well as decision points $($ assessment $)$ ?have zero duration.

$1-1.$ ?How much is the flow time of the buffer $(3$ ?points $)$

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$1-2.$ ?As you know, only some of the customers go through step $3$ ?or $4,$ ?and the total duration of this process will be different for each stream. Knowing this, what is the flow time of this process? Show your calculations $($ not just a final answer $)(3$ ?points $)$

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$1-3.$ ?If in average there are $5$ ?applicants waiting to complete step one, $3$ ?applicants waiting in the buffer, $10$ ?applicants waiting to complete step three, and $2$ ?applicants waiting to complete step four, what is the total inventory of this process. $(3$ ?points $)$

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$1-4.$ ? What is the daily processing rate $($ R $)$ ?for this process, based on the total flow time and total inventory you just caluclated $(3$ ?points $)$

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$1-5.$ ?Now that you have calculated the processing rate of this process, please compare it against the daily arrival rate of those applicants $($ provided in the problem description $).$ ?Is this process able to meet the demand within the course of the day? $(3$ ?points $)$