Problem $2330$ points$]$: You have been asked to interview candidates for an open secretarial position. Each candidate's qualifications for the job can be modeled with a lognormal distribution with a mean of $15$ and a standard deviation of $5.($Hint: you need to compute the parameters $$ and $$ of the lognormal distribution by the above mean and standard deviation.$)$ Unfortunately, you must decide whether to offer the job to each candidate in turn before being able to interview the next candidate. In other words, you will first interview candidate $1$ and then decide whether to make an offer or not. If you do not make an offer to candidate $1,$ then you will interview candidate $2$ and again decide whether to make an offer or not. If you pass candidate $2,$ you will go on to candidate $3,$ and so on$.$ Suppose that if you have not made an offer to the first nine candidates, then you will be forced to accept the ${10}^{th}$ candidate. As$-$

$1$

sume that all offers are accepted. Your objective is to hire a candidate with the highest possible qualifications. To achieve this, you plan to set a minimum acceptable score $($MAS$)$ for each interview. For example, you can decide to accept the first candidate with a score over $8.$ Then, your MAS would be $8$ at each interview. An alternative policy would be to accept over $8$ on the first interview, over $7$ over the second, and so on$.$ In the most general case, you can have nine decision variables: one MAS for each interview.

a$)$ Suppose you use the same MAS for all interviews. Develop a simulation model with Excel and run at least $1000$ iterations to determine the best MAS as much as possible to maximize the expected qualifications of the candidate offered. Show details in an Excel file.

$[15$ points$]$

b$)$ Suppose you use the following linear equation to determine MAS for each interview: MAS $(t)=a+bt,$ where $t$ ranges from $1$ for the first candidate to $9$ for the last one. Develop a simulation model with Excel and run at least $1000$ iterations to determine the best coefficients a and $b$ as much as possible to maximize the expected qualifications of the candidate offered. Show details in an Excel file.

$[15$ points$]$