For check | Applied Sciences homework help

Module 11: Critical Thinking

Staffing Turnover (110 points)

The Corporate Strategic Plan for Dr. Soliman Fakeeh Hospital shows a focus on retaining employees under their Strategic Directive 1: Invest in People & Development (p. 14). (The Corporate Strategic Plan for Dr. Soliman Fakeeh Hospital)

Considering this primary strategic initiative, the hospital recognizes the high cost of employee turnover. Burnout can contribute to staffing turnover as can an exodus of healthcare workers to other countries for better pay and benefits.

Write a paper that addresses the financial costs associated with staffing, including costs associated with recruiting, training and turnover. You will show the calculations for retaining 2 current employees–a doctor and a nurse. You will also show the calculations for replacing these 2 employees if they quit. The relevant costs are shown below.

In your paper discuss both direct and indirect costs. Address the need to increase the number of doctors and nurses and healthcare workers in Saudi Arabia in accordance with SV2030. How can companies address that need?

Please include this information that was obtained by the finance department for the current year:

Nurses make 112 SAR per hour on average. However, the average salary for a physician is approximately 350,000 SAR per year. They normally work 8 hours per day.

Use this information to calculate retaining employees’ cost for one nurse and for one doctor for the next two years. Next, calculate the costs to replace one nurse and one doctor both of whom will have relocating expenses. Some of the costs may not be relevant in your analysis.

Hiring New Staff (Costs = SAR):
Marketing costs per employee: 19,000
Pay for relocation per employee: 19,000
Training per employee: 35,000
Nonproductive hours due to fatigue per employee during training period (current staff) per employee: 210

Retaining Employees:

Productive Time
260 days at 8 hours per salaried employee
224 days at 8 hours a day per hourly employee

Nonproductive Time
Paid Annual Leave: 21 days per employee
EID Leave: 15 days per employee
Sick Leave: 30 days per employee

Your paper should meet the following structural requirements:

The paper should be 4–6 pages in length, not including the cover sheet, reference page and the required excel sheets as an appendix to the assignment.
You must show all your calculations for credit. Your calculations for this assignment must be submitted as an Excel file, identified as Appendix A, and included as part of the Word document submission.
Formatted according to APA and Saudi Electronic University writing standards.
Provide support for your statements with in–text citations from a minimum of three scholarly articles.
One of these sources may be from the class readings, textbook, or lectures, but one must be external.
The Saudi Digital Library is a good place to find these references.

You are strongly encouraged to submit all assignments to the Turnitin Originality Check prior to submitting them to your instructor for grading. If you are unsure how to submit an assignment to the Originality Check tool, review the Turnitin Originality Check Student Guide.

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July 1, 2023

SYSEN533

DeterministicModelingandSimulationExam1

1. (25 pts) Thecompound tanksystemshown in Figure1 consistsof asphericaltank ofradius R1and acylindrical tankofdiameterD2. A liquid ofconstantdensityis fed atavolumetricrateF1in intothetopof aspherical tankandvolumetric rateF2in intothetop ofthecylindricaltank. The sphericalandcylindrical tanks interactthrough thepipeconnectingthem.Theflowrates intotheconnecting pipedepend ontheheightsoftheliquid in thetanks. Thevolumetric flowrate outof thesphericaltank

intothepipeis given byF1out =k1

h1 , whilethevolumetric flow rateoutofthecylindricaltankinto

thepipeis given byF2out =k1

h2 whereh1 and h2 arethe heightsoftheliquid in thesphericaland

cylindrical tanks respectivelyandk1 is thecommonvalvecoefficient.Thecylindricaltank alsohas a

drain on theright-hand sidewhich hasvolumetricflowrateF3out =k2

coefficientfortheright-hand sidedrain.

h2 wherek2 is thevalve

a) Obtain a dynamicmodelthatdescribes theheightsoftheliquid in thetanks. Is this a linearornonlinearmodel?

b) For constantinputflow rates, F1in and F2in, analytically determine thesteady-statevaluesofh1 and

h2. Dotheshapesand dimensionsof thetanksaffectthesteady-statevalues?

Notethatyoudonotneedtosolvethedifferential equations for thesteady stateanalysis.

c) Simulatethesystem and plottheheightsoftheliquidin thetanks versustimeforconstantinputflowratesusing thevaluesgiven in thetablebelow.(Run thesimulation for2000sec)

F1in	2.0 ft3/s	F2in	1.0 ft3/s
R1	10.0 ft	D2	20.0 ft
k1	2.0ft5/2/s	k2	3.0ft5/2/s
h1(0)	4.0 ft	h2(0)	4.0 ft

Figure1.Compound TankSystem

2. (25pts) Chaoticsystemsareones forwhich small changes eventuallylead toresults thatcan bedramaticallydifferent. The Rösslersystemisoneofthesimplestsets ofdifferential equationsthatexhibits chaoticdynamics. In addition totheir theoretical valuein studyingchaotic systems,theRösslerequations areusefulin several areasofphysicalmodeling including analyzing chemicalkineticsforreaction networks. Consider thereaction network:

A1+X2X

k-1

X+Y2Y

k-2

A5+YA2

k-3

X+ZA3

k-4

A4 +Z2Z

k-5

whereX,Y, and Z represent thechemical specieswhoseconcentrationsvaryandA1, A2, A3, A4, and A5 arechemicalspecies whoseconcentrationsareheldfixed bylargechemical reservoirs, serving tokeepthe system outofthermodynamicequilibrium.ki andk-i denote theforward and inversereaction rates.Thesystem of differentialequations thatdescribetheconcentrations x, y, and z(for chemicalspeciesX,Y, and Z) are:

dx =-y-zdt

dy =x+aydt

dz =b-cz+xzdt

a) Simulatethis systemfor a=0.380, b=0.300,and c=4.280with initial conditionsx(0)=0.1,

y(0)=0.2, z(0)=0.3. Run thesimulation for200seconds using a fixed-step size algorithm witha stepsizeof0.001seconds.Plottheconcentrationsx, y, andzversustimeononefigurewiththreesubplots. Additionally, in separategraphs, plotthephase-spaceplots:xversus y,xversusz, and yversus z. Finally,makea3-Dplotof xvs yvszusing theMatlab graphics command "plot3"

b) Illustratethesensitivityofthesolution to variations intheinitial conditions byrepeating thesimulation ofpart(a) withx(0)=0.0999and thenwith x(0)=0.1001. (A0.1%changein thevalueoftheinitial condition in either direction.)Keeptheinitial conditions for y(0) and z(0) thesameas inpart(a). Showthesensitivitybysuperimposing theplots forthenew valuesyouobtain forx(t),y(t),and z(t)with theoriginal plots forxvs t,yvs t,and zvs t. In addition,makeplotsof thedifferences:x(t)– xorginal(t) vst,y(t) –yorginal(t) vst, and z(t) –zorginal(t) vs t.

c) Illustratethesensitivityofthesolution to variations inparametervalues byrepeating thesimulationof part(a)withc=4.280001. [Use theoriginal initial conditions from part(a).]Show thesensitivitywith thesamesetof plotsas in part(b).

Whyisthis systemnon-linear?

Qualitatively describethesensitivity toinitial conditions and parametervalues.

3) (25 pts) Acontinuous stir tank reactor(CSTR)is used toproducea product P fromchemicals Aand B.Thereactionis A+BàP. Ais inexcess andtherateof decompositionofBisgiven by:

rb =

k1 x2

+ 2

(1 k2 x2 )

wherek1and k2areconstants and x2is theproductconcentration.Theequations describing thesystemaregiven by:

1 1 2 2

The parameters are: Cb1 =24.9,Cb2=0.1 ,k1=k2= 1,andu1 =u2 = 1.The initial conditions are: x1(0) =10and x2(0)=0.

a) First, simulatetheequation for x1onlysinceitdoesnot depend onx2.Notethesteady-statevaluethatyou find forx1.

b) Inthemodelforx2, initializetheintegrator for x1to thesteady-statevalue you found in part(a) andinitialize x2(0)=0. Run thesimulation for 1000seconds to determinex2(t)and thesteady-statevalueof x2.

c) Repeatthesimulation for x2 using an initial value x2(0)=10. Notethenewsteady-statevalueyoufindfor x2.

d) Bothof thepreviouscasesarestable.Thereis anothersteadystatecorresponding to everything elsebeingthesameand thesteadystates forx2and x1being x2= 2.793and

x1=100.This is an unstablesteadystate.Demonstratethis bysetting theinitialvalueoftheintegratorforx2tox2(0) =2.80andshowthatthesimulation goesto theuppersteady-statevalue.Repeatthesimulationwithx2(0)=2.79 and showthatitgoes tothelowersteady-statevalue.Thismeansthatanysmall fluctuation willcausethesystemtofalltosteadystateofpart(b)or risetothesteady stateof part(c).

e) Demonstratethatthesteadystatewith x2=2.793is unstablebylinearizing theequation forx2aboutthesteady-statevaluesandshowingthatthelinearsystem thatresultsis unstable. Youcan do this by either solving thedifferential equationor by simulating thesystem witha small initial Dx2.

4) (25 pts) Considerthefollowing linear system

G(s)=-8s+6 2s3 +9s2 +13s+6

For this problem, usea unit step input.

a) Createamodel for this systemusingonly integrators and run itfor10seconds.

b) Replacetheintegratorswith discreteintegratorsand investigatetheeffectof forward, backward,and trapezoidal integratorswith sampling timesof0.01, 0.1, and0.2seconds.

Notethatintheconfiguration parametersyouwillneedtospecify thestepsizeand changetheintegratortodiscretestates only.Also,setallof thesampling times inthevarious blocksequal tothediscretesampling time.

c) For each case, comparethetruesolution tothediscretesolution intwo ways:

(i) Plotthetruesolution (in blue) and discretesolution (in red)ona singleplot.

(ii) Plotthedifferencebetween thetruesolution and thediscretesolution.

If youwantto bereallyfancy, usethesubplotcommand toshowboth plotsin asinglefigure.

d) Computeanestimateof theintegral squareerror foreach caseand createa tableofthesedifferences.

e) Whatconclusionscanyoudrawregarding theaccuracyofthedifferentmethodsand step sizes?