The crimes are solved by Forensics Offices $($FOs$)$ in San Marcos. An FO works on a crime

until it is solved and then it starts working on the next crime. Suppose that there are two FOs

in San Marcos, and each FO has can solve $5$ crimes per month on average. The crimes are

assigned to an FO based on location. The crimes committed in East San Marcos are

assigned to the East FO and the crimes committed in West San Marcos are assigned to the

West FO$.$ Based on past data, on average, there are $3$ crimes committed in East San Marcos

and there are $3$ crimes committed in West San Marcos each month.

Assume that crime solving $($from the moment FO starts working on the crime until the crime

is solved$)$ and the interarrival times of crimes in any side of the town are exponentially

distributed.

a$)$ Explain the queueing system$($s$)$ for crime handling in San Marcos by

defining the customers, arrival rate $($i$.$e$.,\backslash$lambda $),$ server, service rate $($i$.$e$.,\backslash$mu $),$ and use

Kendall$$s notation to define the queueing system$($s$).$

b$))$ For each of the following criteria, explain whether the

current system satisfies it or not. Show what inequality you are referring to when

answering. That is$,$ just yes$/$no answer will not get credits, it is required to explain the

answer by showing what is checked. See the first one as an example. Assume that $1$

week is $0\mathrm{.}25$ month. You will need to create a sheet named $$Part b$$ in your Excel file

with the system information as well as all the required information to answer the

following questions.

i$.$ Each FO should be busy at least $50\%$ of the time on average. Is this

satisfied? Yes, or No$?$ Explain.

i$.$ Yes, this is satisfied. This criterion is asking for $\backslash$rho $>0\mathrm{.}5.$ Based on the

above results, server utilization $\backslash$rho $=0\mathrm{.}6,$ therefore, each FO is busy $60\%$ on

average; hence, this criterion is satisfied.

ii$.$ On average, there should be no more than two crimes waiting to be solved in

overall San Marcos. Is this satisfied? Yes or No$?$ Explain.

iii. At least $50\%$ of the crimes should be handled $($solved$)$ within one week of

being committed. Is this satisfied? Yes or No$?$ Explain.

iv$.$ On average, a crime should be handled within one week after being

committed. Is this satisfied? Yes or No$?$ Explain.

v$.$ On average, an FO should start handling a crime within one week after being

committed. Is this satisfied? Yes or No$?$ Explain.

vi$.$ There should be $2$ or less crimes waiting to be handled in East San Marcis at

least $80\%$ of the time. Is this satisfied? Yes or No$?$ Explain.

c$)$ Now suppose that you want to consider centralizing the FOs based on

cost$.$ The following are the main cost components:

$$ An office costs $$10,000$ per month, regardless of whether it is active or idle.

$$ Each crime handled costs a fixed $$1,000$ in legal fees.

$$ Each crime waiting to be handled incurs $$2,000$ additional per month.

$$ There is a $$1,000$ additional legal fee if the crime is not solved within two

weeks.

Show your calculation in detail by first showing the cost equation in terms of L$,$ Lq$,$

W$,$ Wq$,\backslash$mu $,\backslash$lambda $,\backslash$rho $,$ C in part i$.$ Note that you will not need to use all these. Also, you will

need to create a sheet named $$Part c$$ in your Excel for the centralized system

defined in part iii. For part ii$,$ you can use the values from $$Part b$$ sheet.

i$.$ Give the cost equation for a single system.

ii$.$Calculate the average monthly cost of crime handling in San

Marcos under the current system, i$.$e$.,$ with one FO handling East and one FO

handling West independently.

iii. Now, suppose that both offices are centralized and a crime in San

Marcos, regardless of its location, is assigned to the next available FO$.$

Calculate the average monthly cost of crime handling in San Marcos under

this centralized system.

iv$.$Based on average monthly cost, which system $($current or

centralized$)$ should be used for crime handling in San Marcos?

d$)$ Answer the following discussion questions

independent of each other and without making any calculations. For each, $2-3$

sentences would be sufficient.

i$.$ If the crime rate increases in San Marcos, the legal fee costs will increase.

Yes or No$.$ Explain why.

ii$.$ If an FO office can solve more crimes in a month by hiring additional police

officers, will the time between consecutive crimes decrease, increase, or

remain similar? Explain why.

iii. If crime rate decreases in San Marcos, total office costs will decrease. Yes or

No$?$ Explain why.

Now, you want to design a simulation model to analyze the crime handling in San Marcos.

e$)$ Discuss the classification of the simulation model you should use. That

is$,$ describe whether the simulation should be stochastic or deterministic, then

describe whether the simulation should be static vs$.$ dynamic, and then describe

whether the simulation should be discrete$-$time vs$.$ continuous time. Briefly explain

each description

Show on Excel please